Step 1

If cooking polenta on stovetop: In a medium pot over high heat, combine 4 1/2 cups water, polenta and 1 teaspoon salt. Bring to a simmer, stirring frequently, until thickened, 30 to 40 minutes, depending on how finely the polenta is ground (coarse-ground polenta takes longer).

Step 2

Alternatively, cook polenta in oven: Heat oven to 350 degrees. In a medium Dutch oven or other oven-safe pot over high heat, bring 4 1/2 cups water, polenta and 1 teaspoon salt to a boil. Reduce heat to medium, stirring constantly until the mixture starts to thicken slightly, 3 to 5 minutes. Cover pot and transfer to the oven. Bake for 20 minutes, then give the mixture a stir. If it looks dry, add another 1/2 cup water. Cover the pot once more, and continue to bake for another 20 to 30 minutes.

Step 3

When polenta is thick and creamy, stir in 2 to 4 of the tablespoons butter (depending on how buttery you like it) and the Parmesan. Taste and add more Parmesan and salt, if needed.

Step 4

As the polenta cooks, prepare the vegetables: In a large skillet, heat oil over medium. Add shallots and sauté until tender and golden, 4 to 6 minutes.

Step 5

Stir in garlic and cook for another minute or two, until fragrant and very lightly golden in spots. Add vermouth and cook until alcohol evaporates, about 2 to 3 minutes.

Step 6

Stir in asparagus and peas, and cook until vegetables are glossy, 2 to 3 minutes. Add stock, remaining 2 tablespoons butter and a large pinch of salt, and bring to a simmer. Cook until vegetables are tender and sauce thickens slightly, 2 to 8 minutes. (Thicker asparagus will take longer to soften.) Stir in the mint. Taste and add more salt, if needed.

Step 7

To serve, spoon polenta into bowls, top with vegetables and their sauce, and grind on lots of fresh pepper. Finish with shaved Parmesan.