Beat together eggs and milk in a medium bowl with a fork for about 30 seconds. Set aside.
Heat olive oil in a medium skillet over medium heat. Cook and stir garlic in hot oil for about 1 minute. Add red onion; cook, stirring occasionally, until somewhat translucent, about 2 minutes. Reduce heat to low and add sun-dried tomatoes. Cook and stir until tomatoes are warm and soft, 3 to 5 minutes. Remove from heat.
Heat butter in a large skillet over medium heat. Pour in beaten eggs. Immediately top with tomato mixture; season with salt and pepper. Sprinkle with Parmesan cheese, oregano, thyme, and basil. Cook for 1 to 2 minutes, slowly folding in the edges of egg as it begins to set underneath. Continue cooking over medium-low heat, folding and stirring eggs until scrambled and mostly set, 2 to 3 minutes more.