Noodles
1) Place in a medium bowl: 1 cup flour, 1 egg, and a dash of salt. Mix these ingredients with a fork, then sprinkle in small amounts of cold water. Sprinkle a little water, mix, sprinkle a little water, mix, and so on, until the dough forms a ball. Then start playing with the dough with your hands. Knead it, punch it, squeeze it, pat it. At first, it will likely be sticky. Sprinkle more flour into the bowl and work the flour into the dough with your fingers. Keep alternating between sprinkling flour and kneading it until the ball has absolutely no stickiness remaining. Then pat it into a 6-inch disk. Do you notice a little stickiness on either side of the disk? If yes, you need to work more flour into the dough. I know it would be simpler to give exact measurements of what works. But the moisture is variable and makes a difference in the climate you live in and the exact size of your egg and the exact measurement of the flour. This method of using your hands to feel for the right consistency works best. In the meantime, enjoy the fine motor workout your hands get -- pretend you're a kid playing with play-doh.
2) Get a good-sized wooden cutting board and sprinkle flour generously all over the board. Start rolling out your 6-inch disk with a rolling pin. Keep flipping the dough and rubbing flour on it. When the dough starts to get too big for the cutting board, cut the dough in half and set that half aside on a plate to roll out later. Continue rolling out the first half until the dough is quite thin and shaped like a large rectangle. Remember to keep flipping it and rubbing more flour onto it. There's a lot of flour involved in this whole pasta-making business, but I have learned the hard way that if you have any stickiness in your dough, it will just lump together into a gooey mess. When you are satisfied with the rectangle you rolled out, let the dough rest a few minutes. Then rub a generous amount of flour across the surface of the dough. Roll up the dough into a log, cinnamon-roll style. Take a sharp knife and cut the log into 1/4-inch wide strips, to look like miniature cinnamon rolls. Unroll your strip and hang them up on a pasta drying rack. You can tap the noodles to shake off some of the excess flour. Take the second half of your dough and finish it like you did the first half. It is possible to cut the noodles into 1 & 1/2-inch lengths at this point and cook them in your soup, but I find that letting them dry for awhile allows them to be more manageable and less likely to stick together.
3) Allow the noodles to dry for several hours. If they become dry enough to break apart, break them up into 1&1/2 inch lengths. If they're not dry enough to break, cut them into the shorter strips.
4) ALTERNATIVE short-cut: Whatever you do, DON'T use ramen noodles! I tried this once for guests and by the time everyone finally settled down for the meal, the noodles were quite swollen and soggy. Yuck. If you want to bypass the fun part of making the noodles or just don't have time, get frozen egg noodles or a good quality dry noodles. Most standard pastas you find at the stores don't work quite right--they taste like they're meant for an Italian dish and don't have that all-American homemade egg noodle taste. The one brand of dried pasta I have found that tastes somewhat close to my homemade version is: Rustichella D'Abruzzo -- fettucine style. Break up this pasta into shorter lengths.
Soup
1) Cook chicken, salt and pepper, chicken bouillon, chopped fresh parsley, paprika, and diced yellow onion in a big pot of simmering water until chicken is well-done. Remove chicken and cut or shred into bite-sized pieces. Add back to the pot of water. If you use chicken that has skin and bones, you will get the best flavor for your broth, but it will still taste good if you choose to use boneless, skinless chicken.
2) While the chicken is cooking, prep/cut/chop the remaining vegetables: carrots, celery (including leaves), and tomatoes. After the chicken is cooked, add the carrots and celery. When the carrots and celery are cooked, add the tomatoes and the noodles. Stir frequently to ensure the noodles don't stick. When the noodles are cooked, taste the soup and tweak it again with salt, pepper, paprika, and/or bouillon to get just the right flavor.
Grilled Chicken Version
I haven't done this in years, but I've used grilled chicken in my soup before, and that smokey flavor makes the soup taste out of this world. I'm drooling just thinking about it!
Vegetarian Version
This soup is also good using (frozen) Quorn Chik'n pieces instead of real chicken. Use vegetarian based bouillon.
