Summer Squash Gratin

​2  tablespoons extra virgin olive oil
½  medium onion, chopped (about 1 cup chopped)
2  plump garlic cloves, minced
1 ½  pounds summer squash, cut in 1/2-inch dice
1  small red pepper, cut in 1/4-inch dice
 Salt and freshly ground pepper
2  tablespoons chopped fresh parsley
2  large or extra-large eggs
½  teaspoon salt
 Freshly ground pepper
½  cup low-fat milk
1  cup cooked rice 
1  teaspoon coarsely chopped fresh thyme leaves
2  ounces Gruyère cheese, grated (1/2 cup, tightly packed)
1  ounce freshly grated Parmesan (1/4 cup, tightly packed)

Heat the olive oil in a large, heavy skillet over medium heat and add the onion. Cook, stirring often, until tender, 5 to 8 minutes, and add the garlic, summer squash, red pepper, and about 3/4 teaspoon salt. Turn the heat to medium-high and cook, stirring, until the squash is translucent and the red pepper tender, about 10 minutes. Add freshly ground pepper, taste and adjust salt. Stir in the parsley and remove from the heat. 
Preheat the oven to 375ºF. Oil a 2-quart baking dish with olive oil. In a medium bowl, beat together the eggs, salt, pepper, and milk. Stir in the rice, thyme, the sautéed squash and the cheeses. Scrape into the baking dish.
Bake 35 to 40 minutes, until nicely browned on the top and edges. Remove from the oven and allow to stand for at least 10 minutes before serving, or allow to cool. The gratin is good hot, warm, or room temperature.