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1
Preheat the oven to 375 degrees .
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2
Place racks in the lower and middle thirds of the oven.
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3
Drizzle the garlic with olive oil, wrap it tightly in foil and roast on the bottom rack of the oven for 50 minutes.
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4
Lightly rub the potatoes with olive oil, prick them all over with a fork and bake on the lower rack for 45 minutes, until fork-tender.
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5
Line a large baking sheet with foil.
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6
Add the squash and rub with olive oil.
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7
Bake on the upper rack for about 30 minutes, stirring once, until soft.
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8
Squeeze the roasted garlic cloves out of their skins into a small bowl and mash to a paste.
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9
Peel the hot potatoes and pass them through a ricer into a large bowl.
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10
Add the hot squash to the ricer and pass it into the bowl with the potatoes.
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11
Let cool slightly.
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12
Add the egg yolks, ricotta, parsley, 1 tablespoon of salt and 1 tablespoon of the mashed roasted garlic (reserve any extra for another use).
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13
Stir until combined.
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14
Sprinkle on the 1 1/4 cups of flour and gently stir it in.
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15
Scrape the dough onto a floured surface and knead gently until smooth but still slightly sticky.
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16
Line a baking sheet with wax paper and dust with flour.
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17
Cut the gnocchi dough into 5 pieces and roll each piece into a 3/4-inch-thick rope.
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18
Cut the ropes into 1/2-inch pieces and transfer the gnocchi to the baking sheet.
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19
Lightly oil another baking sheet.
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20
In a large, deep skillet of simmering salted water, cook half of the gnocchi until they rise to the surface, then simmer them for 1 to 2 minutes longer, until cooked through.
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21
Using a slotted spoon, transfer the gnocchi to the baking sheet.
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22
Repeat with the remaining gnocchi.
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23
In a large nonstick skillet, melt the butter over moderate heat and cook until golden brown, about 2 minutes.
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24
Add the sage and thyme and cook for 20 seconds.
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25
Add the gnocchi and cook for 1 minute, tossing gently.
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26
Season with salt and serve, passing the cheese shavings at the table.
