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1
Bring stock and milk to a boil in a heavy-bottomed pot over medium-high heat; whisk constantly.
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2
Slowly pour polenta into the liquid in a thin stream, whisking continuously to prevent lumps from forming.
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3
Reduce heat to low and stir constantly with a wooden spoon for 25 minutes, scraping the bottom and sides, until polenta pulls away from the pot sides and is very thick.
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4
Remove from heat; stir in butter and Parmigiano Reggiano until fully incorporated.
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5
Season with salt and pepper to taste.
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6
Pour onto a wooden board or into a shallow dish to set, or serve immediately as creamy polenta in bowls drizzled with olive oil.