In a large stock pot melt butter over medium heat. Add minced onions and garlic. Cook until onions become translucent. Add celery and carrots. Cook for 5 minutes. Add pheasant to the stockpot and lightly brown on all sides- no more than 1 minute per side.
Add the chicken base and water (or chicken stock). Bring to a boil, lower heat and allow soup to simmer for at least 1 hour. Add salt and pepper to taste.
10 minutes before adding the dumpling batter mix the egg noodles into the soup.
Mix up the dumplings. Add together all dry ingredients- flour, baking powder, salt and cayenne pepper. Add wet ingredients and stir together. It should be a moist, stiff batter- if not all the dry ingredients are moist add another 1/4 of milk.
Drop dumpling batter into the pheasant soup by the spoonful until all the batter covers the soup. Cover the pot and allow to sit and cook for an additional 10 to 15 minutes or until dumplings are completely cooked through.