Put a baking sheet on the middle oven rack and preheat to 375 degrees F. Toss the squash with the melted butter, 1/4 teaspoon salt and a few grinds of pepper; spread in a single layer on the hot baking sheet. Roast until just tender, about 15 minutes. Stir in the shallot and roast until softened, about 5 minutes. Let the squash cool for a few minutes on the baking sheet.
Meanwhile, place the phyllo shells on another baking sheet. Bake until crisp, about 5 minutes. Mix the cream cheese and mayonnaise in a medium bowl.
Fill each phyllo shell with a teaspoon of the cream cheese mixture. Top with a few cubes roasted squash and sprinkle with the smoked cheddar and thyme. Return to the oven and bake until lightly browned, about 15 minutes.