Preheat the oven to 375°F. Using a serrated bread knife, remove the crusts from the bread (it is not important to be perfect about it). Slice the bread, then cut into 1/4-inch cubes until you have about 3 cups. In a medium skillet, heat the butter over medium heat until melted and lightly browned. Add the garlic and saute briefly until light brown. Add the sage, bread cubes, and salt and pepper to taste and toss well. Scatter on a baking sheet. They should be in a fairly tight single layer. If they are too loose, they will cook too rapidly and dry out. Bake, stirring several times, until crisp on the outside but still chewy inside, about 10 minutes. (The croutons can be made a day or so ahead of time and stored in an airtight container at room temperature.)

Using a mandoline or serrated paring knife, slice the tomatoes as thinly as possible and arrange in overlapping circles on each of 4 plates. Season with salt and pepper. Just before serving, in a nonreactive bowl, mix the croutons with the tomato sauce and Parmesan. Do not mix ahead of time or the bread will get soggy. Pack about one-fourth of the tomato mixture into an individual 3-inch mold, such as a tea cup or tart pan, and unmold onto one of the prepared plates. Repeat with the remaining mixture.

Place the arugula in a bowl, add the vinaigrette and salt and pepper to taste, and toss to coat evenly. Arrange the arugula on top of each portion of the tomato mixture.

With a vegetable peeler, shave the ricotta salata evenly over the tops of the salads. Serve immediately.