Place tomatoes on baking sheets lined with paper towels; sprinkle with 1 teaspoon salt. Let stand for 30 minutes. Pat dry. Let stand for 30 minutes, and pat dry again.

Heat oil in a 10-inch skillet over medium heat. Add onion; cook, stirring occasionally, until lightly browned around edges, 5 to 7 minutes. Transfer onion to a small bowl, and let cool completely.

Roll All-Butter Pie Dough into a 12-inch circle (about 1/8 inch thick).

Lightly grease a 9-inch deep-dish pie plate, and press dough into bottom and up sides. Roll edges under, and crimp as desired. Freeze for 15 minutes, or refrigerate for 30 minutes.

Position oven rack in bottom third of oven. Preheat oven to 425°.

Stir together onion, 1½ cups cheese, mayonnaise, egg, thyme, pepper, and remaining 1 teaspoon salt in a medium bowl. Spread half of onion mixture in bottom of prepared crust. Sprinkle with 2 teaspoons bread crumbs. Arrange half of tomato slices, overlapping slightly, on top. Repeat layers with remaining onion mixture, remaining 2 teaspoons bread crumbs, and remaining tomatoes.

Bake for 20 minutes. Reduce oven temperature to 375°. Top with remaining ½ cup cheese, cover edges with foil, and bake until lightly golden brown, center is set, and an instant- read thermometer inserted in center registers 175°, 30 to 35 minutes more.

Let cool on a wire rack for at least 2 hours.

Garnish with thyme, if desired.

Serve at room temperature. Cover and refrigerate for up to 2 days.