Drizzle the corn with 1 tablespoon of the oil. On a greased grill pan over high heat, grill the corn, turning on all sides, until cooked and slightly charred, about 15 minutes.
Preheat the oven to 425 degrees F. In a large bowl, combine the bread cubes, butter, paprika, garlic powder, 1/4 teaspoon salt and 1/8 teaspoon pepper. Gently toss until all the bread is coated with the butter mixture. Spread on a baking sheet and bake until toasted and golden brown, 8 to 10 minutes. Let cool.
Slice the kernels off the corn cobs. In a large bowl, combine the corn, tomatoes, baby greens, toasted bread cubes, 1/4 teaspoon salt and 1/8 teaspoon pepper. Drizzle with the remaining 2 tablespoons of oil, the white wine vinegar, 1/4 teaspoon salt and 1/8 teaspoon pepper and toss.
Plate the salad and top with the shaved Parmesan.