To make the croutons: preheat the oven to 350ºF. Cut the baguette into 1/2" cubes. Spread the bread cubes on a rimmed baking sheet pan and bake until golden brown, 4 to 5 minutes. Set aside.
To make the vinaigrette: whisk together the Garlic, Dijon mustard, balsamic vinegar and sherry vinegar in a small bow. Mix together the corn oil and extra virgin olive oil, then slowly whisk it into the vinegar mixture. Season with salt and pepper. Set aside.
Separate the Radicchio leaves and soak them in cold water for 10 minutes, or longer if necessary. Drain and dry (with a lettuce spinner if you have one). Cover with a damp towel and refrigerate until ready to use.
To serve: combine the Radicchio, croutons, vinaigrette and 1/3 cup of the parmesan cheese in a large bowl, tossing well so each leaf is coated with vinaigrette. Divide the salad among 4 chilled places and sprinkle with the remaining parmesan cheese. Serves 4.