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1
In a small bowl, beat 1 of the eggs.
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2
Cut the puff pastry in half crosswise.
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3
On a lightly floured work surface, roll out 1 piece of puff pastry to a 12-inch square.
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4
Cut a 1/2-inch strip from each edge of the pastry.
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5
Brush the edge of the pastry square with some of the beaten egg.
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6
Place the strips around the edge to make a raised border.
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7
Chill for 30 minutes.
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8
Repeat with the second piece of puff pastry.
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9
Meanwhile, preheat oven to 450.
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10
Using a large, sharp knife, cut off the ends of the squash until you reach the seeds.
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11
Scoop out and discard the seeds.
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12
Carefully slice the acorn squash crosswise into 1/4-inch thick rings.
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13
Arrange the rings on 2 rimmed baking sheets.
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14
Mix 2 teaspoons of the olive oil with the butter and honey and brush on the squash rings; season with salt and pepper.
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15
Bake for 15 minutes, or until the rings are browned on the bottom.
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16
Reduce the oven temperature to 375.
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17
In a medium bowl, mix the ricotta with the remaining egg and the heavy cream.
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18
Season with 3/4 teaspoon kosher salt and a generous pinch of pepper.
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19
In a medium skillet, heat the remaining 2 teaspoons of olive oil.
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20
Add the shallots and cook over moderately high heat, stirring occasionally, until golden.
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21
Stir in the sugar.
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22
Brush the raised pastry borders with some of the beaten egg.
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23
Spread the ricotta filling in the pastry squares.
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24
Arrange the squash rings on top, browned sides up.
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25
Scatter the shallots over the tarts and bake for 30 minutes, or until the pastry is golden brown.
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26
Sprinkle the tarts with toasted pumpkin seeds and serve warm.
