How to Make It
Stir together ricotta, mozzarella, 1/2 cup Parmigiano-Reggiano, 1/4 cup chopped basil, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a medium bowl. Chill until ready to use.
Place 1 dough sheet on a well-floured surface with one long side facing you. Brush right half of dough lightly with water; arrange one-fourth of whole basil leaves on top in a single layer. Fold the dry dough half over the basil-topped dough half; press gently to adhere. Dust dough generously with flour, and cut in half crosswise.
Set rollers of a pasta machine to setting number 4. Working with 1 basil-filled dough piece at a time, feed dough through pasta machine. Transfer to a lightly floured surface with one long side facing you; brush off excess flour. Repeat process with the second basil-filled dough piece.
Leaving a 1-inch edge from the short side of the first dough sheet, place a teaspoon-size ball of ricotta filling 1/2 inch from the bottom of the long side. Continue placing spoonfuls of ricotta filling in 1 row, leaving 2 inches between them. Lightly brush dough around ricotta filling with water. Fold top half of dough over row of ricotta filling, and gently press dough around filling to seal. Using a fluted pasta wheel cutter or a sharp knife, cut filled dough into 2-inch square ravioli. Transfer to a lightly floured baking sheet; cover with plastic wrap, and chill until ready to use. Repeat process with second basil-filled dough piece and ricotta filling.
Repeat steps 2 through 4 with remaining 3 dough sheets, whole basil leaves, and ricotta filling. Ravioli can be refrigerated up to 8 hours or overnight, or frozen up to 1 month.
Working over a large bowl, grate tomatoes on the large holes of a box grater, discarding skin and stem. (If mixture is very loose, pour through a fine wire-mesh strainer into a bowl; discard excess liquid.) Add 2 tablespoons salt, remaining 1/2 cup chopped basil, and remaining 1/2 teaspoon pepper. Let stand at room temperature 15 minutes. Gradually whisk in oil.
Bring 4 quarts water to a boil over high. Add remaining 1/4 cup salt, and stir until dissolved. Working in batches, boil ravioli until tender, about 1 minute and 30 seconds. (If cooking from frozen, boil ravioli 2 to 3 minutes.) Serve ravioli over fresh tomato sauce and sprinkled with remaining 1/2 cup Parmigiano-Reggiano. Drizzle with balsamic glaze, if desired.