Preheat oven to 400°F. Slice beets off stems; set stems and greens aside. Toss beets with 1 Tbsp. of the oil in a 13x9" baking dish. Pour in just enough water to cover bottom of the pan. Cover tightly with foil and roast for 60 minutes, until beets are tender. Let beets cool, then rub off skins with a kitchen towel. Cut beets into wedges and set aside.
Rinse beet stems and greens thoroughly. Finely chop most of the stems, leaving about 2 to 3 inches attached to greens.
Heat remaining 3 Tbsp. oil in a large sautè pan over medium. Add red pepper flakes; cook 1 to 2 minutes, stirring often, until fragrant. Add garlic and chopped beet stems; cook 7 to 8 minutes, stirring occasionally, until softened. Add beet greens; cook additional 7 to 8 minutes, stirring often, until greens are wilted and remaining stems are tender. Season with 1/4 tsp. of the salt and black pepper.
While greens cook, prepare polenta by bringing 4 cups of water and remaining 1 tsp. salt to a boil in a large saucepan. Gradually whisk in cornmeal. Continue whisking until mixture is smooth and begins to thicken. Reduce heat to low and cook until tender and thickened, but still creamy, stirring often, about 15 minutes. (If mixture gets too thick or clumpy, whisk in additional 1 to 2 Tbsp. water or milk.) Stir in cheese, butter, and herbs.
Divide polenta evenly into each of 4 bowls. Distribute beet green mixture evenly over polenta. Top evenly with beet wedges. Garnish with additional cheese, if desired.