There are about a gazillion recipes for chicken and chicken noodle soup. Without tasting the soup you've described it would be hard to offer a specific suggestion. However, here's a chicken noodle soup that I like. Bessie liked Goodman's egg noodles.
Grandma Bessie’s Chicken Noodle Soup
3 - 4 quarts cold water, approx.
2 medium sized chickens, cut up
2 medium sized onions, quartered
2 med-large carrots, peeled and quartered
2 large celery stalks cut in 2-3 inch lengths
1 large clove garlic, bruised
10 or 12 black peppercorns
2 medium sized Turkish bay leaves
3 - 4 sprigs parsley
1 pkg small egg noodles
Take chicken thighs, drumsticks, necks and backs and put into a baking pan or large, heavy skillet. Place in 375° F. oven for about ½-hour or so; do not cook through. Fillet and skin the breasts, remove as much fat as possible, or as much as you like, wrap them well and reserve them in the fridge.
Take the chicken from the oven at the end of 30 minutes, remove from skillet and set aside for a while to cool. Scrape up any brown crust and add to the stockpot. When chicken parts have cooled enough to handle, crack the leg bones and put all chicken parts, breast bones, neck, skin etc., except the breast fillets, into the stockpot. Add all the other ingredients except the peppercorns and parsley. Cover with cold water, about 3 or 4 quarts.
Bring the pot to boil and reduce heat to a slow-medium simmer. Watch the pot and skim off any foam that forms. Simmer, partially covered for 3 - 4 hours. At the last hour add the peppercorns and parsley. Remove from heat and let cool enough to handle. Strain through a double layer of dampened cheesecloth, pressing out as much liquid as possible. Place stock, in a covered bowl, into the refrigerator and let stand overnight.
The next day remove the breasts and the stock from the fridge; thinly julienne the breasts along the grain. If breasts are large, cut strips in half. Scrape off all the fat from the stock. The stock should be gelatinous, so this wll be easy. Any fat that you can't scrape off can be removed with a paper towel slightly dampened with warm water.
Cook egg noodles about 1/2 done according to package directions, remove from heat, drain through large strainer or colander. Toss while draining so noodles don't stick, set aside. Put the stock back into stockpot and bring to a boil.
When stock boils add the noodles, wait for stock to come to second boil, add the sliced chicken breasts, stir, wait for stock to boil reduce heat and simmer, partially covered until chicken breasts are done. Serve immediately, season to taste with salt and pepper. You should have a very rich, flavorful stock and nice juicy breast meat.
Note: I have since modified the instruction somewhat. Instructions that haven’t changed should be left the same.
Place a circular cake cooling rack on the bottom of the stock pot. Blanch the chicken in boiling water for just a few minutes and rinse it well, then remove and fillet the breasts. Rinse the stock pot. After roasting, return the chicken to the pot atop the cooling rack, set the heat on low and slowly bring the liquid to simmer. Do not let the stock boil. Don’t add the vegetables immediately, but after about two hours of actual simmering time. Cut the vegetables in smaller pieces than called for in the original recipe. When the chicken and vegetables are done cooking, remove the pot from the heat and let cool slightly, then immerse the pot about 3/4 the way or more in a sink filled with cold water (iced water is best). Be careful not to let the sink water run into the stock pot. After about ½ hour or so, remove the pot from the sink, strain the stock and refrigerate, covered.