Mix goat cheese, Parmesan, herbs, garlic, and lemon juice in a small bowl; season with salt and pepper. Transfer to a pastry bag fitted with a small round tip (or use a resealable plastic bag and snip one corner of bag open with scissors). Pipe mixture into olives.
Place olives, thyme sprigs, chiles, and lemon zest in a shallow dish and pour oil over top.
Olives can be marinated 4 days ahead. Cover and chill. Bring to room temperature before serving.
Recipe by Rita Sodi & Jody Williams
Photograph by Eva Kolenko