In a large pot (I use a dutch oven), melt the butter over medium heat. Add the onions, carrots, potatoes, salt, and pepper. Cook for 2 to 3 minutes, stirring often, until the vegetables start to soften.
Add the chicken broth and diced chicken breasts. Cover pot, turn up heat to bring to a simmer, and cook for 10-15 minutes (adjusting heat if needed to maintain a gentle simmer) until chicken is cooked through and veggies are tender.
In a small bowl, combine the ½ cup water and ¼ cup flour and whisk until smooth. Whisking vigorously, slowly add the flour mixture into the hot broth and stir until well combined. Stir in the frozen peas and heavy cream and bring the soup back to a gentle simmer.
For the dumplings, in a medium bowl, whisk together the dry ingredients. Add the sour cream, milk and oil. Stir just until combined, being careful not to overmix.
Drop teaspoon-sized amounts of dumpling dough (I use a #60 small cookie scoop) into the boiling soup, covering the entire surface of the soup. Keep the dumplings fairly small as they will expand while cooking.
Cover the pot and let the soup and dumplings simmer gently for 12-15 minutes. Avoid the temptation to lift the lid of the pot while the dumplings cook or you will lose all that lovely steam that helps the dumplings puff up and taste amazing.
After the time is up, check dumplings. Cover pot and continue cooking a few minutes longer if needed until dumplings are completely cooked through. Remove the lid and stir the dumplings gently to break them apart. Then serve.
