Preheat the oven to 400°F. Lightly oil a small baking dish for the polenta and line a rimmed baking sheet with parchment for the salmon and asparagus.

In the baking dish, whisk together the polenta, broth, milk, water, 1 tablespoon olive oil, 1/2 teaspoon kosher salt, and a few grinds of pepper. Cover tightly with foil and bake for 30 minutes.

While the polenta starts baking, toss the cherry tomatoes, shallot, unpeeled garlic cloves, capers, balsamic vinegar, 1 tablespoon olive oil, 1/4 teaspoon salt, and pepper in a small oven-safe dish. After the polenta has baked for 10 minutes, place the tomato dish in the oven and roast alongside it for 22 to 25 minutes, until the tomatoes are collapsed and glossy.

Uncover the polenta, whisk it vigorously to smooth out any lumps, then stir in the mascarpone and half of the Parmigiano-Reggiano. Return it to the oven uncovered for 8 to 10 minutes, until creamy, thick, and bubbling lightly at the edges. Remove and keep warm.

Meanwhile, make the crust by mixing the panko, pine nuts, lemon zest, parsley, remaining Parmigiano-Reggiano, 1 tablespoon olive oil, a pinch of salt, and several grinds of pepper in a small bowl.

Place the salmon fillets on the prepared baking sheet. Rub the tops with 1 teaspoon olive oil, season with salt and pepper, and press the panko mixture evenly over the top of each fillet.

Toss the asparagus on the same baking sheet with the remaining 2 teaspoons olive oil, a pinch of salt, and pepper. Roast the salmon and asparagus for 10 to 13 minutes, until the crust is golden, the salmon flakes easily at the thickest part, and the asparagus is tender with browned tips.

While the salmon roasts, finish the sauce: squeeze the roasted garlic from its skins into the tomato mixture, then mash the tomatoes, shallot, garlic, and capers with a fork until saucy but still textured. Stir in the softened butter and basil until glossy. Taste and add a few drops more balsamic vinegar, salt, or pepper as needed.

Let the salmon rest for 3 minutes. If the polenta has tightened, whisk in a splash of hot water or milk until spoonable.

Spoon the baked mascarpone polenta onto two warm plates. Add the asparagus, set the crusted salmon on top, and spoon the roasted tomato basil butter around and partly over the fish. Serve with lemon wedges.