Whisk mustard, vinegar, shallot, and 1/4 cup olive oil. Season with salt and pepper.
Heat grill to high. Slice polenta into thirds lengthwise, drizzle with olive oil, and season with salt and pepper. Grill polenta until lightly charred, 2 minutes per side, then cut into croutons. Drizzle romaine and radicchio with olive oil and season with salt and pepper. Grill lettuces, cut sides down, until slightly wilted and charred, about 1 minute. Arrange greens and croutons on a platter and drizzle with vinaigrette.