How to Make It
Bring 4 cups water and 1¼ teaspoons salt to a boil in a medium pot over high. Slowly whisk in polenta. Reduce heat to medium-low and cook, whisking often, until no lumps remain and polenta begins to pull away from sides of pot, 8 to 10 minutes. Remove from heat and stir in 1 tablespoon oil and ½ teaspoon pepper.
Brush a large rimmed baking sheet with 1 tablespoon oil. Pour polenta onto baking sheet and spread to a ¼-inch-thick oval. Let cool slightly, cover loosely with plastic wrap, and chill until firm.
Preheat oven to 400°F with rack in lowest position. Brush top of polenta with 1 tablespoon oil. Bake until edges are golden brown and crisp, 45 to 50 minutes.
Meanwhile, heat remaining 2 tablespoons oil in a large skillet over medium-high. Add sausage; cook, breaking it up with a wooden spoon, until no longer pink, about 5 minutes. Add chard stems and cook until tender, about 2 minutes. Add chard leaves and remaining ¼ teaspoon each salt and pepper. Toss until wilted, about 2 minutes.
Top polenta with tomatoes, breaking them up as you go, sausage, and chard. Dollop cheese over top. Bake until cheese and greens begin to brown, 12 to 15 minutes. Serve immediately.