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1
In a small bowl stir together garlic and oil and let stand 15 minutes.
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2
With a mandoline or other manual slicer, slice squash crosswise into 1/16-inch thick rounds, transferring to plate.
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3
Prepare grill: Open vents in lid and bottom of kettle grill and put 25 briquets on 2 opposite sides of bottom, leaving middle clear.
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4
Oil rack and position with wider openings over briquets.
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5
Light briquets.
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6
(They will be ready for cooking as soon as they turn grayish-white, 20 to 30 minutes.)
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7
Remove plastic wrap from 2 pieces of rolled-out-pizza dough (if grill is not large, work with 1 piece at a time, keeping remaining piece chilled) and lightly brush dough with some garlic oil.
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8
Trying not to stretch dough, carefully transfer it, oiled side down, with your hands to rack of grill.
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9
(If it's a very hot day, the dough may get too soft to transfer easily; if so, pop it into the freezer until firm again, about 15 minutes.)
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10
Lightly brush top with some garlic oil.
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11
When grilling pizzas, rotate them if 1 side of grill is hotter than the other.
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12
Grill crusts, covered, until undersides are golden brown on bottom, about 4 minutes.
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13
Flip crusts over with 2 metal spatulas and top each crust with half of cheeses, squash, and thyme.
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14
Lightly brush pizzas with some garlic oil and grill, covered, about 5 minutes, or until undersides are golden brown and cheeses are melted.
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15
Garnish pizzas with thyme sprigs and cut into wedges.
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16
In a large bowl stir together 1/3 cup water, yeast, and sugar and let stand until foamy, about 10 minutes.
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17
Stir in remaining 1/3 cup water, 2 tablespoons oil, 1 3/4 cups flour, cornmeal, and salt and blend until mixture forms a dough.
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18
Knead dough on a floured surface, incorporating as much of remaining 1/4 cup flour as necessary to prevent dough from sticking, until smooth and elastic, 5 to 10 minutes.
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19
Alternatively, dough may be made in a food processor.
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20
Proof yeast as described above.
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21
In food processor process yeast mixture with 1 3/4 cups flour, cornmeal, and salt until mixture forms a ball, adding more water, 1 teaspoon at a time, it too dry or more flour, 1 tablespoon at a time, if too wet, and knead dough by processing 15 seconds more.
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22
Put dough, prepared by either method, in an oiled deep bowl and turn to coat with oil.
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23
Let dough rise, covered with plastic wrap, in a warm place 1 hour, or until doubled in bulk, and punch down.
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24
Form dough into 4 balls.
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25
Makes enough dough for four 10-inch thin-crust pizzas.
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26
Lightly brush a baking sheet with olive oil.
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27
On a lightly floured surface roll out 1 ball of dough 1/8 inch thick (about 10 inches in diameter).
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28
Brushing off excess flour, transfer dough with your hands to baking sheet and cover surface completely with plastic wrap.
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29
Repeat procedure with remaining dough balls and plastic wrap in same manner, stacking rolled-out pieces on top of one another on baking sheet.
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30
Wrap baking sheet with more plastic wrap to ensure that dough is completely covered.
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31
(Chill dough until firm, about 1 hour, and up to 4 hours.)
