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1
Preheat the broiler and position a rack 8 inches from the heat.
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2
In a bowl, combine the oil and garlic.
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3
Brush the eggplant slices with 1 1/2 tablespoons of the garlic oil, arrange on a broiler pan and season lightly with salt and pepper.
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4
Broil the eggplant for about 8 minutes, turning once, until tender and deep golden.
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5
Transfer to a platter to cool.
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6
Repeat the process with the summer squash, using 1/2 tablespoon of the garlic oil and broiling for about 6 minutes.
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7
In a medium bowl, toss the shiitakes and red pepper with the remaining 1 tablespoon of garlic oil and season with salt and pepper.
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8
Arrange the pepper, skin side up, on the broiler pan and add the shiitakes.
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9
Broil for about 6 minutes, turning the shiitakes once, until the mushrooms are tender and golden and the pepper skin is charred.
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10
Add the shiitakes to the platter.
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11
Transfer the pepper to a small bowl, cover with plastic wrap and let steam for 15 minutes.
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12
Peel the pepper and cut it into thin strips.
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13
Line a large sturdy baking sheet with parchment paper.
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14
Cut the puff-pastry sheet in half to form two 10-by-4-inch rectangles.
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15
On a lightly floured surface, roll the pastry to form two 14-by-5-inch rectangles, about 1/8 inch thick.
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16
Set the pastry rectangles on the prepared baking sheet and refrigerate them until firm.
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17
Preheat the oven to 375.
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18
Arrange the cheese on the pastry, leaving a 1-inch border.
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19
Arrange the eggplants, shiitakes and squash on the cheese and crisscross the pepper strips on top.
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20
Fold the pastry sides up and pinch the corners.
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21
Refrigerate until the pastry is firm, about 10 minutes.
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22
Bake the tarts for about 40 minutes, or until they are puffed and golden and the bottoms are cooked.
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23
Let cool slightly on the baking sheet, then transfer to a rack.
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24
Cut the tarts crosswise into 2-inch slices and serve warm or at room temperature.
