Melt the butter in a skillet over medium-high heat. Add the scallops and garlic. Cook, stirring, until the scallops are just cooked through and liquid reduces, about two minutes. Add the dill and cook 30 seconds more. Transfer mixture to a bowl and let cool. Add the cheese to the scallops and stir to combine.

Preheat broiler. Place the toasted baguette slices on a broiler pan. Top each slice with the scallop mixture. Broil the crostini a couple of inches from the heating element until the bread begins to brown along the edges and the cheese melts, about two to three minutes. Transfer to a platter and let cool slightly before serving.