Arrange racks in the upper and lower thirds of the oven; preheat to 425 degrees. Line a large rimmed baking sheet with foil and brush with 1 tablespoon oil. Arrange polenta rounds on the oiled sheet.
Very coarsely chop (do not puree) half the tomatoes in a food processor. Cut the remaining tomatoes in half (quarter if large). Combine the tomatoes in a bowl with 4 tablespoons oil and the remaining ingredients. Toss to coat.
Stack 3 24x12 inch sheets of parchment paper on another baking sheet. (Don't use foil--the tomato acid will react with aluminum.) Spoon the tomato mixture onto one side of the stacked parchment. Fold the parchment layers over the mixture and crimp the edges tightly to form a sealed packet.
Place the baking sheet with the tomato packet on the upper rack and the sheet with the polenta on the lower rack. Bake, turning polenta rounds once, until the polenta is light golden and the tomatoes are saucy (carefully open the packet to check; steam will escape), 25-30 minutes. (You can also cook the polenta on a grill pan or on a charcoal or gas grill).