Cook the tortellini according to the package directions.
Meanwhile, cook the bacon in a large skillet over medium heat until crisp, 7 to 8 minutes. Reserve the bacon and discard the drippings.
Wipe out skillet and return to medium heat. Add the butter and melt, swirling or stirring with a wooden spoon as it starts to foam and sputter. Remove the butter from the heat as soon as it begins to turn golden brown and smells nutty, about 1 minute.
Break the bacon into small pieces and add to skillet with the arugula, salt, pepper, and cooked tortellini. Toss well and divide among individual bowls.
Tip: If you can't find arugula, try this dish with spinach, basil, or watercress.