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1
Preheat oven to 400F, with racks in upper and lower thirds.
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2
On a rimmed baking sheet, toss tomatoes with 2 tablespoons oil, oregano, and 2/3 of the garlic; season with salt and pepper.
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3
Brush another rimmed baking sheet with 1 tablespoon oil.
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4
Arrange squash in one layer, season with salt and pepper.
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5
Roast squash until tender, about 20 minutes, and tomatoes until slightly shriveled, about 40 minutes, rotating sheets halfway through.
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6
In a blender, puree the tomato halves.
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7
Season with salt and pepper; set aside.
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8
In a large skillet, heat 1 tablespoon oil over medium-high heat.
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9
Add remaining garlic and cook, stirring, for 30 seconds.
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10
Gradually add the spinach and toss until wilted, about 4 minutes.
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11
Transfer spinach to a strainer and press to release liquid.
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12
When cool, chop spinach and season with salt and pepper.
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13
In a large bowl, mix ricotta, 1/4 cup Parmesan, egg, and nutmeg until smooth; season with salt and pepper.
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14
Lightly oil a 9-inch square baking dish.
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15
Spread 1/4 of the tomato sauce in dish, top with 3-4 noodles, breaking to fit as needed.
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16
Top with half the ricotta mixture, the squash, 1/4 of the tomato sauce, and 3-4 noodles.
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17
Top with remaining ricotta mixture, cooked spinach, 1/4 of the sauce, and 3-4 noodles.
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18
Top with remaining sauce, the mozzarella, and 1/4 cup Parmesan.
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19
Set rack in the middle of oven.
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20
Bake on a rimmed baking sheet until golden brown, about 30-35 minutes.
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21
Let cool 15 minutes before serving.
