Gather your large skillet, a sharp knife, and a cutting board. Pat the shrimp dry and season lightly with salt and pepper. Heat 1 tablespoon of butter over medium heat until it melts and begins to foam.
Add the sliced mushrooms to the skillet and sauté until they turn golden and soft, about 5 minutes, filling the kitchen with a savory aroma. Stir in the minced garlic and cook for another 30 seconds until fragrant.
Push the mushroom mixture to one side of the pan. Add the remaining 2 tablespoons of butter to the cleared space, then place the shrimp in a single layer. Cook for about 2 minutes per side, until they turn pink and opaque, gently flipping with tongs.
Pour in the dry Marsala wine, carefully scraping up any browned bits from the bottom of the pan with a wooden spoon. Let the wine simmer and reduce by half, about 3-4 minutes, until the sauce becomes glossy and slightly syrupy.
Sprinkle the flour over the sauce and stir well to help thicken it slightly. Add the chicken broth and stir to combine, allowing the sauce to simmer for another 2 minutes until it's smooth and velvety.
Taste the sauce and adjust seasoning with a pinch of salt and pepper if needed. Turn off the heat and let the dish rest for a minute so flavors meld. Serve the shrimp and mushroom sauce immediately over pasta, rice, or crusty bread, garnished with fresh herbs if desired.
