Preheat the oven to 375°F and line a baking sheet with parchment paper.
Slice each jalapeño in half lengthwise and remove the seeds and membranes.
In a mixing bowl, stir together the cream cheese, Monterey Jack cheese, and garlic powder until smooth.
Spoon the cheese mixture into each jalapeño half, filling them level with the edges.
Lay one sheet of phyllo dough on a clean surface and brush lightly with melted butter. Cut the sheet into 1/2-inch strips.
Wrap the strips around each stuffed jalapeño, overlapping slightly to create a mummy-bandage look and leaving a small gap near the top for the filling to show.
Place the wrapped peppers on the baking sheet and brush the phyllo with any remaining butter.
Bake for 18 to 22 minutes until the phyllo is golden and crisp.
Let the mummies cool for 3 minutes before serving.