Rinse eggplant; trim off and discard stems. Cut eggplant into 1/2-inch cubes.
In a 5- to 6-quart pan over high heat, combine eggplant, garlic, onion, 1 cup broth, and 4 tablespoons basil. Cover and bring to a boil. Boil, stirring often, until eggplant mashes very easily when pressed, 20 to 25 minutes.
Meanwhile, in a 4- to 5-quart pan over medium-high heat, bring pasta sauce and remaining broth to boiling, stirring often. Add tortellini and stir often until pasta is barely tender to bite, about 5 minutes. Remove from heat. Stir in jack cheese and 6 tablespoons parmesan cheese.
Butter sides and bottom of a 9-inch cheesecake pan with removable rim. Dust pan with bread crumbs. Spoon 1/2 of the tortellini mixture into pan and spread level. Top tortellini with eggplant, spread level, then add remaining tortellini and spread level. If making ahead, cover and chill up to 1 day.
Bake, covered, in a 350° oven for 20 minutes (50 minutes if chilled). Uncover and bake until hot in center (about 130° on a thermometer), 10 to 15 minutes longer. Let stand 10 minutes.
Run a knife between pan rim and pasta; remove pan rim. Sprinkle pie with remaining parmesan cheese and basil. Cut into wedges.