In a Dutch oven set over medium heat, melt the butter with the onions and garlic. Cook for 2-3 minutes, then add the 1/3 cup flour. Mix in the thyme, sage, cayenne, carrots, celery, and mushrooms. Toss to coat. Pour over 6 cups of vegetable broth and season with 1 teaspoon salt and 1/2 teaspoon black pepper.
Cover and cook over medium heat for 10 minutes, until the vegetables are tender.
To make the dumplings, in a separate bowl, stir together 1 1/2 cups flour, 2 teaspoons baking powder, 1/2 teaspoon dried sage, and season with 1/4 teaspoon pepper. Add 1 cup milk. Mix until just combined.
Bring the soup to a gentle boil. Drop a heaping tablespoon of the dough into the soup, adding about 6 dumplings at a time. Cover and cook for 10 minutes, until the dumplings are cooked through and puffy.
If desired, add 2 tablespoons salted butter to a small skillet set over medium-high heat and allow the butter to brown. Divide the soup and dumplings between bowls. Serve topped with brown butter, fresh thyme, flaky salt, and black pepper. Enjoy!
Serve immediately and enjoy this cozy meal!