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1
Soak the Polenta
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2
Put the polenta in a 4-quart heavy-duty saucepan and whisk in the boiling water. Cover and let sit at room temperature for at least 8 and up to 12 hours.
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3
Cook the polenta
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4
In a 2-quart saucepan, bring the broth to a boil. Whisk the broth and 1 tsp. salt into the polenta, loosening it and breaking up any clumps. Bring to a boil over medium-high heat, whisking once or twice, about 5 minutes.
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5
Turn the heat down to maintain a simmer and continue cooking, whisking constantly, until the polenta thickens from soupy to porridge-like, about 2 minutes.
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6
Turn the heat down to low. Cover and cook, stirring vigorously and scraping the bottom of the pan with a wooden spoon or spatula every couple of minutes. When you can see the bottom of the pan as you drag the spoon across it, 5 to 10 minutes later, begin tasting the polenta; it's done when it's thick, creamy, and tender. It should be granular, but not gritty.
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7
While the polenta cooks, pulse the basil, parsley, and marjoram in a food processor until finely chopped, about seven 1-second pulses; don't overprocess into a paste.
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8
Remove the polenta from the heat, and stir in the cheeses, butter, chopped herbs, and 1/2 tsp. pepper until the butter is melted. Season to taste and serve right away, passing more Parmigiano at the table.
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9
Make Ahead Tips
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10
After soaking the polenta at room temperature, you can refrigerate it, covered, for up to 2 days.