Melt 2 tablespoons of butter in a large skillet over medium-high heat. Add the mushrooms and cook for 3–4 minutes, stirring occasionally, until lightly browned and beginning to soften.
Reduce the heat slightly. Add the remaining 2 tablespoons of butter followed by the flour. Stir until the flour and butter form a smooth paste around the mushrooms.
Add the minced garlic, drained sun-dried tomatoes, Italian seasoning, and paprika. Stir for about 30–60 seconds, just until the garlic becomes fragrant.
Gradually whisk in the chicken broth, making sure the flour mixture blends smoothly into the liquid. Add the heavy cream and Parmesan cheese.
Simmer gently, stirring frequently, until the sauce becomes creamy and starts to thicken. Avoid boiling vigorously so the cream remains smooth.
Stir the fresh basil into the Marry Me Mushrooms. Add red pepper flakes if desired, then season with salt and black pepper to taste.
Remove from the heat and garnish with additional fresh basil and a small sprinkle of red pepper flakes. Serve warm over pasta, mashed potatoes, or rice.