In a medium bowl, whisk together the eggs, thyme and 1 teaspoon salt. In a nonstick 12-inch skillet over medium, melt 1 tablespoon of butter. Add the shallots, ½ teaspoon salt and ¾ teaspoon pepper. Cover and cook, stirring occasionally, until the shallots are lightly browned, about 5 minutes. Add the tomatoes and cook, uncovered and stirring occasionally, until the tomatoes have softened and started to brown, 5 to 7 minutes. Transfer to a small bowl and wipe out the pan.