Place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 1 inch. Cover the saucepan and bring the water to a boil over high heat. Remove from the heat and let the eggs stand in the hot water for 15 minutes. Drain. Cool the eggs under cold running water. Peel once cold. Halve the eggs lengthwise and scoop the yolks into a bowl. Mash the yolks together with pressed garlic with a fork.
Cook the bacon in a large, deep skillet over medium-high heat until evenly browned, about 10 minutes. Drain on a paper towel-lined plate; chop once cool. Add to the mashed egg yolks. Stir the basil, mayonnaise, red pepper flakes, salt, and pepper into the mixture until evenly mixed. Fill the egg white halves with the mixture; sprinkle each stuffed egg with a bit of paprika.