Position a rack in the center of the oven and preheat it to 350 F.
In a small skillet over medium heat, cook bacon until crispy, about 8 minutes. Remove to a paper towel-lined plate and reserve.
While the bacon is cooking, in a medium sized bowl, whisk together the eggs, milk and Parmigiano-Reggiano. Season with salt and pepper.
In a large bowl, toss the bread cubes, tomatoes, basil, mozzarella and reserved bacon. Mix to combine. Set aside until ready to bake
Rub the inside of 4 ramekins with butter. Scoop bread mixture into each ramekin, pressing down so it all fits tightly. Carefully pour the egg mixture over everything.
Place ramekins on a rimmed baking sheet. Bake uncovered until puffed and golden brown, and a knife inserted into center comes out clean, about 40-45 minutes. (Ramekins can be stuffed ahead of time and put in the refrigerator. They'll need an extra 10-15 minutes to bake.) Let stand for a few minutes.
In a medium bowl, toss arugula, lemon juice, olive oil, salt and pepper. Top each ramekin with some arugula and serve.