Melt 2 tablespoons of butter in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced yellow onion and sauté for 4 to 5 minutes until soft, translucent, and sweet.

Add the remaining 2 tablespoons of butter and turn heat up to medium-high. Add the sliced cremini mushrooms, dried dill weed, fresh thyme, salt, and black pepper. Sauté without disturbing for 2 to 3 minutes to encourage deep golden browning, then stir occasionally for another 6 to 8 minutes until all mushroom juices have released and evaporated.

Stir in the minced garlic and cook for 60 seconds until fragrant. Sprinkle in the sweet Hungarian paprika and all-purpose flour. Stir continuously for 90 seconds, coating the mushrooms evenly to gently toast the flour and bloom the paprika aromatics without scorching.

Slowly pour in the vegetable broth and soy sauce while whisking or scraping the bottom of the pot to lift all caramelized browned bits (fond). Slowly stir in the warm whole milk until smooth.

Bring the soup to a gentle simmer over medium heat. Reduce heat to medium-low and let it simmer uncovered for 8 to 10 minutes, stirring occasionally, until the liquid thickens into a glossy, velvety consistency.

Temper the sour cream: Ladle about 1/2 cup of hot soup into a heat-safe bowl with the room-temperature sour cream and whisk vigorously until smooth. This prevents curdling when introduced to the pot.

Remove the pot from the heat. Whisk the tempered sour cream and fresh lemon juice into the soup until fully integrated, silky, and rich. Taste and adjust with extra salt or freshly ground black pepper if needed.

Ladle into warm bowls. Garnish with a fresh dollop of sour cream, a scattering of fresh chopped parsley and dill, and serve immediately alongside warm toasted sourdough baguette for dipping.