Place stock and dried porcini mushrooms in a large saucepan; bring to a boil over high. Remove from heat; let steep, uncovered, for 30 minutes. Strain mushrooms through a fine mesh strainer into a heat proof bowl. Set stock and mushrooms aside.

Meanwhile, melt 2 tablespoons butter in a large Dutch oven or similar large pot over medium-high. Add half of the fresh mushrooms and ½ teaspoon salt; cook, stirring occasionally, until browned, 8 to 10 minutes. Transfer to a plate; repeat with 2 tablespoons butter and remaining half of the fresh mushrooms and ½ teaspoon salt. Transfer to plate. (Do not wipe Dutch oven clean.)

Melt remaining 2 tablespoons butter in Dutch oven over medium-low. Add onion; cook, stirring occasionally, until softened and translucent, about 5 minutes. Add flour, thyme, paprika, and garlic; cook, stirring constantly, until slightly darkened in color, about 3 minutes.

While stirring constantly, gradually add chicken stock mixture and Worcestershire to Dutch oven. Bring to a simmer over medium-high; reduce heat to medium-low, and stir in reserved fresh and rehydrated mushrooms. simmer, stirring occasionally, until slightly thickened and flavor meld, about 15 minutes. Stir in heavy cream.

Place sour cream in a small bowl, and stir in 3 tablespoons of simmering broth mixture from Dutch oven, 1 tablespoon at a time. Remove broth mixture from heat, and stir in sour cream mixture and dill. Divide evenly among 4 bowls. Garnish with additional sour cream and dill.