Unroll crust into a 9-in. pie plate; flute edge. Refrigerate 30 minutes. Preheat oven to 400°.
Line unpricked crust with a double thickness of foil. Fill with pie weights, dried beans or uncooked rice. Bake on a lower oven rack until edges are golden brown, 10-15 minutes. Remove foil and weights; bake until bottom is golden brown, 3-6 minutes longer. Cool on a wire rack. Reduce oven setting to 325°.
In a large skillet, heat oil over medium-high heat. Add leeks and mushrooms; cook and stir until tender, 3-5 minutes. Add sausage and garlic; cook 1 minute longer. Remove from the heat. Sprinkle 1/2 cup cheese over crust. Top with sausage mixture and tomatoes. Whisk eggs, cream, sour cream, thyme, salt and pepper; pour over top. Sprinkle with remaining cheese.
Bake until a knife inserted in center comes out clean, 40-45 minutes. Cover edges with foil during the last 15 minutes to prevent overbrowning if necessary. Let stand 10 minutes before serving. If desired, top with additional fresh thyme.