Heat oil in a large nonstick or cast iron skillet over high heat. Add bell pepper and sauté 3-4 minutes, until crisp-tender. Transfer the pepper to a plate. Sauté the beef in the hot skillet over high heat, and cook just until no longer pink, about 2 minutes. With a slotted spoon, transfer the beef to the plate with the peppers. 

Add the lime juice, honey, hoisin sauce, soy sauce, ginger, and crushed red pepper to the skillet, and whisk to combine with the pan juices. Bring to a boil and cook over high heat, stirring often, for 5-6 minutes, unti the liquid reduces to about 1/3 cup. Return the beef and bell pepper back into the skillet and toss with the sauce, until heated through, about 30 seconds. 

Serve hot.