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1
Line 15x10-inch rimmed baking sheet with foil.
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2
Combine 4 cups water and 1 teaspoon salt in heavy large saucepan.
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3
Bring to boil.
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4
Gradually add polenta, whisking until smooth.
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5
Reduce heat to medium-low; cook until polenta thickens and pulls away from sides of pan, whisking frequently, about 30 minutes for polenta and 15 minutes for yellow cornmeal.
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6
Whisk in butter and 1 teaspoon oregano.
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7
Pour out polenta onto prepared baking sheet; spread evenly to edges of sheet.
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8
Chill until firm, at least 2 hours or overnight.
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9
Preheat oven to 300F.
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10
Line another large baking sheet with parchment paper.
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11
Arrange tomato slices in single layer on prepared sheet.
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12
Sprinkle tomatoes with 1/2 teaspoon sugar, then some salt.
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13
Drizzle with 2 tablespoons oil.
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14
Roast until tomatoes are tender but sides are firm and slices still hold together, about 2 hours.
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15
Cool.
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16
(Polenta and tomatoes can be made 1 day ahead.
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17
Cover separately and chill.)
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18
Preheat oven to 450F.
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19
Line another large baking sheet with parchment paper.
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20
Using 1 3/4- to 2-inch-diameter cookie cutter, cut out 24 rounds from polenta.
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21
Place rounds in single layer on prepared sheet.
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22
Top each round with 1 tomato slice.
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23
Sprinkle with remaining 1 teaspoon oregano.
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24
Top each with 2 or 3 olive halves.
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25
Drizzle with remaining 2 tablespoons oil, then sprinkle with Parmesan.
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26
Bake polenta pizzas until heated through and cheese melts, about 10 minutes.
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27
Serve warm.