1. Preheat oven to 375oF. Line a large rimmed baking sheet with parchment.
2. In a small bowl combine the olive oil and syrup. Briefly set aside.
3. Slice the acorn squash in half lengthwise. Use a spoon to scoop out the seeds. Slice each half crosswise into ½-inch half moons. Brush the squash on both sides with the olive oil mixture and sprinkle with kosher salt. Roast for 20 minutes, turning the squash over halfway through the cooking time.
4. Line 2 baking sheets with parchment. Gently roll out the puff pastry on a lightly floured surface to smooth it out. (Aim for something about 12” by 10.”) Transfer each sheet of pastry to the prepared baking sheets. Gently score a ½-inch border around the edge with a paring knife. Pierce the pastry all over inside the border with a fork to help release steam while the pastry bakes. Brush both with a little olive oil.
5. Transfer the puff pastry to the oven and bake for 15 minutes. Remove from the oven.
6. To assemble each tart: Top with 1 cup Fontina inside the scored border. (If the pastry has puffed up inside the border, simply flatten it slightly with a spatula.) Sprinkle with ½ teaspoon thyme and top with half the prosciutto. Add 1 ounce goat cheese and 6 slices of squash.
7. Return tarts to the oven and bake for 20 minutes until the pastry is lightly browned and the prosciutto has crisped around the edges.
8. Finish the tarts with the remaining goat cheese and the pomegranate arils.
9. Slice each tart into 12 pieces with a sharp knife or pizza cutter. Serve warm or at room temperature.