In a large pot, melt 1 tablespoon of unsalted butter over medium heat. Add the diced sweet onion and cook until it becomes translucent, about 5 minutes. Then, stir in the diced carrots and minced garlic, seasoning with kosher salt and pepper to taste. Cook for an additional 3-4 minutes until the carrots start to soften.
Sprinkle the dried dill over the sautéed vegetables and mix well. Pour in the 5 cups of chicken stock and add the halved baby Yukon gold potatoes. Bring the mixture to a gentle boil, then reduce the heat and let it simmer until the potatoes are tender, about 15-20 minutes.
Once the potatoes are cooked, take 1 tablespoon of all-purpose flour and mix it with a small amount of cold water to create a slurry. Stir the slurry into the pot to thicken the chowder. Add the cup of frozen corn and simmer for another 5 minutes.
Stir in the cup of heavy cream and gently fold in the salmon chunks. Cook for about 5-7 minutes, or until the salmon is cooked through and flakes easily. Taste and adjust the seasoning with more salt and pepper if needed.
In a mixing bowl, combine 1 cup of all-purpose flour, 2 teaspoons of baking powder, a pinch of kosher salt and pepper, 1 teaspoon of dried dill, 1 teaspoon of dried chives, and 1 teaspoon of garlic powder. In another bowl, whisk together the lightly beaten egg and 1/2 cup of milk. Pour the wet ingredients into the dry ingredients and mix until just combined.
Using a spoon, drop spoonfuls of the dumpling batter into the simmering chowder. Cover the pot and let the dumplings steam on top of the chowder for about 10 minutes or until they are fluffy and cooked through.
Once the dumplings are ready, ladle the chowder into bowls, topping each serving with sliced green onions. Enjoy your warm and comforting Salmon Chowder with Dill Dumplings!