In a small bowl, beat 1 of the eggs.

On a lightly floured work surface, roll out 1 piece of puff pastry to a 12-inch square. Cut a ½-inch strip from each edge of the pastry.

Brush the edge of the pastry square with some of the beaten egg to act as glue. Place the strips around the edge to make a raised border.

Repeat with the second piece of puff pastry. Chill for 30 minutes.

Meanwhile, preheat oven to 450° F. Cut off the top and the bottom of the squash. Scoop out and discard the seeds (or roast them with a little salt and eat them as a snack). Slice the acorn squash into 1/4-inch thick rounds. Arrange the rounds on baking sheets. Mix 2 teaspoons of the olive oil with the butter and maple syrup and brush on the squash rings; season with salt and pepper.

Bake for 15 minutes, or until the rings are browned on the bottom. Reduce the oven temperature to 375°.

In a medium bowl, mix the ricotta with the remaining egg and the milk. Season with ¾ teaspoon sea salt and a generous pinch of pepper.

In a medium skillet, heat the remaining 2 teaspoons of olive oil. Add the shallots and cook over moderately high heat, stirring occasionally, until golden. Stir in 1 tablespoon maple syrup.

Brush the chilled, raised pastry borders with some of the beaten egg to make it shiny. Spread the ricotta filling in the pastry squares.

Arrange the squash rings on top, browned sides up. Scatter the shallots over the tarts.

Bake for 30 minutes, or until the pastry is golden brown.

Drizzle the tarts with honey (I have this really robust honey called abbamele and a pine cone syrup that are dark and savory that are amazing with this tart- but any full flavored honey will do) or pomegranate molasses and serve warm.