Preheat oven to 375 degrees F (190 degrees C). Arrange tart shells in 2 muffin tins; line shell each with a layer of pie weights or dried beans.
Bake shells in the preheated oven until edges of crusts are lightly browned and about 75% cooked, 5 to 10 minutes.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes.
Drain bacon slices on paper towels; crumble when cooled.
Divide 1 cup Swiss cheese, bacon, and green onions evenly into the tart shells.
Whisk eggs, milk, mustard, salt, and black pepper together in a bowl. Ladle egg mixture into each tart shell about 2/3 full. Top each tart with the remaining 1/4 cup Swiss cheese.
Bake in the preheated oven until egg is set in the middle of each tart and shells are browned, 25 to 30 minutes.