Heat a large nonstick skillet over medium-high heat. Add 1 tablespoon oil; swirl to coat. Add zucchini, shallots, and 1/4 teaspoon salt; sauté 5 minutes or until tender and beginning to brown lightly. Add corn and thyme; sauté 1 minute. Remove from heat; cool slightly.
Weigh or lightly spoon our into a dry measuring cup; level with a knife. Place our, cornmeal, 1/2 teaspoon salt, and 3/4 teaspoon pepper in a food processor; pulse 2 times to combine. Combine 1/3 cup oil and 1/4 cup milk. With processor on, gradually add oil mixture through food chute; process until dough is crumbly. Sprinkle dough into a 9-inch pie plate coated with cooking spray; quickly press dough into an even layer in bottom and up sides of pan. Bake crust at 400°F for 15 minutes or until edgesare lightly browned. Remove from oven.
Reduce oven temperature to 350°F.
Spoon zucchini mixture into warm crust; sprinkle evenly with cheese. Combine 2/3 cup milk, eggs, 1/2 teaspoon salt, and 1/4 teaspoon pepper; stir well with a whisk. Pour egg mixture over filling in crust. Bake at 350°F for 40 to 45 minutes or until a knife inserted in center comes out clean and top is lightly browned. Cool 10 minutes on a wire rack before cutting into wedges.
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