Frisée and Roasted-Potato Salad

1 1/2 lb small boiling potatoes, cut into wedges 1 large garlic clove, finely chopped 7 tablespoons olive oil 1 shallot, finely chopped 1 1/2 tablespoons Sherry vinegar or red-wine vinegar 1 1/2 teaspoons Dijon mustard 1 teaspoon kosher salt 3/4 lb mixed greens such as frisée (French curly endive), mizuna, baby spinach, and mesclun, coarse stems discarded 3 tomatoes, halved horizontally, seeded, and cut into thin wedges 1/4 cup finely grated Parmigiano Reggiano