Pat shrimp dry with paper towels and toss in flour. Season with salt and pepper. Set aside on a plate.
Bring a large pot of salted water to a boil and cook tortellini according to package directions. Drain, toss in a bit of olive oil to prevent sticking, cover, and set aside.
Melt butter over medium heat in a large skillet. Toss mushrooms into the skillet and season to taste with salt and pepper. Cook until mushrooms release their liquid and turn a deep golden brown, about 8-10 minutes. Remove about 3/4 of the mushrooms from the pan onto a plate.
Add 1tbsp oil to the skillet. Set shrimp into skillet and cook for 2 minutes on one side, then flip and cook another 2 minutes until pink and firm. Set on plate with the reserved mushrooms. Stir shallots, garlic, and thyme until fragrant, about 1 minute. Pour in marsala wine and broth. Bring to low simmer and cook until liquid reduces by half, about 5-8 minutes.
Add mushrooms and shrimp back to the cooking liquid. Stir in milk until sauce thickens. Remove pan from heat and stir in tortellini. Taste for salt and pepper. Enjoy!