Place a large cast iron skillet over medium-high heat and add a tablespoon of butter. Once melted and shimmering, add the sliced onions and minced garlic, sautéing until fragrant and golden, about 3-4 minutes.
Add the sliced wild mushrooms to the skillet, spreading them out so they cook evenly. Let them brown deeply, stirring occasionally, until they release their water and develop a rich, smoky aroma and deep brown color, about 8-10 minutes.
Sprinkle the flour over the mushrooms, stirring well to coat evenly. Cook for about 1 minute to eliminate the raw flour taste and help thicken the sauce later.
Gradually pour in the warm broth, stirring constantly to create a smooth, velvety sauce. Bring to a gentle simmer and cook until the mixture thickens slightly, about 5 minutes. The sauce should be glossy and cling to the mushrooms.
Reduce the heat to low and stir in the smoked paprika, then fold in the sour cream off the heat to prevent curdling. Mix until the sauce is smooth, creamy, and aromatic. Season with salt and pepper to taste.
Let the stroganoff rest for a couple of minutes so the flavors meld and the sauce thickens further. The mushrooms should be deeply browned, and the sauce velvety and inviting. Serve hot, garnished with fresh herbs if desired, alongside crusty bread or over noodles.