In large skillet, heat half of the oil over medium-high heat; cook garlic, thyme, salt and pepper for 4 minutes, stirring often.
Add mushrooms and stir occasionally, cooking until softened, about 4 minutes.
Add wine and cook until absorbed.
Transfer to food processor. Add olives, capers, parsley, and remaining oil. Pulse until blended but still chunky.
Serve cool or at room temperature, refrigerate up to 4 days.