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1
Line an 11- by 7-inch baking pan with foil, leaving a slight overhang on all sides.
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2
In a heavy saucepan bring water with salt to a boil and add polenta in a thin stream, whisking.
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3
Cook polenta over low heat (it should be barely boiling), stirring constantly, until very thick, about 10 minutes.
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4
Spread polenta evenly in pan.
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5
Separately mince shallots and garlic and chop arugula.
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6
In a non-stick skillet cook shallots in oil over moderate heat, stirring occasionally, until softened, about 5 minutes.
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7
Add garlic, arugula, and salt to taste and cook, stirring, a few seconds, or until arugula is just wilted.
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8
Spread arugula mixture evenly over polenta and cool to room temperature.
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9
Chill polenta, covered, until firm, at least 2 hours, and up to 1 day.
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10
Preheat oven to 400F.
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11
Sprinkle arugula topping evenly with Parmesan, pressing gently to make it adhere, and, using foil, transfer polenta to a cutting board.
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12
Cut polenta lengthwise into thirds and cut strips crosswise into 3/4-inch-wide canapes.
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13
Arrange canapes on a large baking sheet and bake in upper third of oven 10 minutes, or until just heated through.
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14
Change oven setting to broil and broil canapes 2 minutes, or until tops just begin to brown.
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15
Serve canapes warm or at room temperature.
