Melt 2 tablespoons of butter in a large heavy-bottomed Dutch oven or soup pot over medium-high heat. Add the sliced mushrooms in a single layer and cook undisturbed for 4-5 minutes until deeply browned on the bottom. Stir and continue cooking until mushrooms release their moisture and caramelize (about 8 minutes total). Transfer 1/3 of the sautéed mushrooms to a small bowl to reserve for garnish.

Lower heat to medium and add the remaining 2 tablespoons of butter to the pot along with the diced onion. Sauté for 4-5 minutes until soft, translucent, and fragrant. Stir in minced garlic and cook for 60 seconds.

Sprinkle the sweet Hungarian paprika, dried thyme, and all-purpose flour over the caramelized mushrooms and onions. Stir continuously for 90 seconds to toast the flour and bloom the paprika essential oils, creating a deeply fragrant, crimson-colored roux coating the vegetables.

Slowly pour in the chicken bone broth and soy sauce, whisking vigorously to dissolve any browned fond from the bottom of the pot. Bring to a gentle boil, then lower heat to medium-low and simmer uncovered for 10 minutes until slightly thickened.

Pour in the whole milk and simmer gently for another 5 minutes over low heat (do not let it boil violently).

Place the sour cream in a small heatproof bowl. Ladle about 1/2 cup of the hot soup into the sour cream and whisk vigorously until smooth (this tempers the cream and prevents curdling). Pour the tempered sour cream mixture back into the soup pot, stirring to combine into a velvety, creamy emulsion.

Stir in the fresh lemon juice and chopped fresh dill. Season with salt and black pepper to taste. Remove from heat.

Ladle hot soup into warm ceramic bowls. Top each serving with the reserved sautéed mushrooms, an extra swirl of sour cream, a pinch of sweet paprika, and fresh dill sprigs. Serve immediately alongside warm, thick slices of crusty sourdough bread!