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1
Combine mayonnaise, basil, and lemon juice in processor.
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2
Blend until smooth (some basil bits will remain).
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3
Season mayonnaise with salt and pepper.
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4
Transfer to small bowl, cover, and refrigerate.
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5
(Can be made 2 days ahead.
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6
Keep refrigerated.)
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7
Rinse 2 mini muffin pans (12 cups per pan) with cold water; shake off excess water.
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8
Mix tomatoes, garlic, and oil in medium bowl; sprinkle with salt and pepper.
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9
Let stand 15 minutes.
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10
Arrange 4 tomato quarters in bottom of each prepared muffin cup.
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11
Bring 2 1/2 cups water and salt to boil in heavy large saucepan over medium-high heat.
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12
Gradually whisk in polenta.
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13
Reduce heat to medium and cook until polenta thickens, whisking almost constantly, about 10 minutes.
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14
Reduce heat to low and continue to cook until polenta is tender, whisking often, about 15 minutes longer.
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15
Whisk in cheese and butter.
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16
Season polenta to taste with pepper.
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17
Spoon enough polenta into muffin cups to cover tomatoes and fill cups.
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18
Using wet fingertips, press polenta firmly to compact.
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19
Cover pans with waxed paper; let stand until polenta is firmly set, at least 30 minutes and up to 2 hours.
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20
Cut around each tartlet to loosen.
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21
Turn over muffin pans, releasing tartlets.
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22
Arrange, tomato side up, on platter.
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23
Top each with dollop of basil mayonnaise.
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24
Serve, passing remaining mayonnaise.
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25
*Sold at Italian markets, natural foods stores, and some supermarkets.
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26
If unavailable, substitute an equal amount of regular yellow cornmeal, and cook mixture for about half the time.
