Wash all the escarole and tear 1 pound into bite-size pieces. Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat until hot. Stir in the garlic, 3/4 teaspoon salt and 1/2 teaspoon pepper. Cook, stirring, until the garlic is golden, about 2 minutes. Stir in the torn escarole, a handful at a time, and cook, turning with tongs and adding more escarole as the greens wilt. Cook, stirring occasionally, until the liquid evaporates, about 5 minutes. Stir in the hot sauce.
Place 4 tortillas on the work surface. Spread 1/2 cup of the cheese evenly over each tortilla, then divide the escarole among the tortillas, spreading evenly. Sprinkle the escarole with 1/2 cup more cheese per tortilla, spreading evenly. Top with the remaining tortillas.
Wipe out the skillet. Heat 1 tablespoon of the oil over medium heat. Place 1 quesadilla in the skillet and cover. Cook until the bottom is golden, 2 to 3 minutes. Flip the tortilla and cook until the other side is golden, 2 to 3 minutes more. Transfer the quesadilla to a work surface and cook the remaining quesadillas in the same manner.
Cut the remaining escarole into thin shreds. Add the beans, tomatoes, lime juice, cumin, the remaining 1 tablespoon oil and 1/2 teaspoon each salt and pepper.
Cut the quesadillas into wedges and serve with the bean and escarole salad and salsa.