Preheat oven to 400°. Divide beets between 2 large sheets of foil. Drizzle ½ Tbsp. olive oil over beets on each sheet; season with vinegar, kosher salt, and pepper and wrap up foil around beets. Roast on a rimmed baking sheet until tender, 40 to 50 minutes. Let cool slightly and transfer the residual beet/oil/vinegar liquid into a large bowl. Then, using a paper towel, rub skins from beets (they should slip off easily). Crush beets with the bottom of a small bowl (it’s alright if they fall apart).
Meanwhile, whisk quark and lemon juice together and place in refrigerator.
Heat 3 Tbsp. olive oil in a large skillet over medium-high heat. Add onions, season with kosher salt and pepper, and cook until nicely charred, about 4 minutes per side. Transfer to the large bowl (which has the residual beet/oil/vinegar liquid from the previous step), add ¼ cup mint and 2 Tbsp. dill, and toss to coat. Generously smear quark on each plate, neatly place the beets & onions and drizzle the juices from foil – this is the lovely red combination of vinegar and beets. Add the dill, salt, and pepper. Serve at room temperature.