In a small saucepan over low heat, melt the butter with the garlic until fragrant.
Lay 1 sheet of phyllo dough on a work surface, brush it all over with the melted butter, sprinkle with a little Parmesan and chopped parsley, top with another sheet and repeat 3 more times until 4 sheets have been used. Cover the phyllo dough with a damp kitchen or paper towel while it sits on the counter to prevent it from drying out as you work. Repeat the stack with the remaining sheets so you end up with 2 stacks. With a large chef knife, cut each stack into 12 equal pieces, 4 by 3 inches. Lightly spray a mini muffin pan with nonstick cooking spray. Line each muffin cup with 1 of the phyllo pieces, gently pressing it down into the edges to form a cup. Repeat to make 24 mini phyllo caps.
Bake in a preheated oven for about 10 minutes or until light golden brown and crisp. Remove from oven and cool completely before filling.