Toss the broccoli slaw, radishes and 2 tablespoons cilantro in a large bowl. Add the lime juice and 1 tablespoon olive oil; season with salt and pepper and toss. Set aside.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the beef, chili powder and cumin and season with salt and pepper. Cook, breaking up the meat, until browned, 2 to 3 minutes. Stir in the salsa. Transfer the mixture to a bowl and stir in the remaining 2 tablespoons cilantro; set aside. Wipe out the skillet.
Spread the beef mixture on one half of each tortilla and top with the cheese; fold in half to cover the filling. Heat 1/2 tablespoon olive oil in the skillet over medium heat. Add 2 quesadillas and cook until the cheese melts and the tortillas are golden, 2 to 3 minutes per side. Transfer to a cutting board. Repeat with the remaining 1/2 tablespoon olive oil and quesadillas.
Cut the quesadillas into wedges. Serve with more salsa and the broccoli slaw.
Photograph by Ryan Dausch