Pat the shrimp very dry. Season both sides with salt and pepper.
Melt 2 tablespoons of the butter with 1 tablespoon olive oil until the butter browns slightly. Add the shrimp (do not overcrowd the pan) and cook for 2 minutes per side, until golden. Remove to a plate.
Add the remaining 4 tablespoons of butter. Melt until browned, about 2 minutes longer. Stir in the garlic and thyme for 1 minute, then pour in the wine and bring to a simmer until slightly reduced, about 2-3 minutes longer. Stir in the lemon juice.
Throw the shrimp back into the skillet, as well as the parsley. Toss to warm through.
Serve with pasta, polenta, or potatoes, as desired.