Combine mayonnaise, sour cream, 1/4 cup cilantro, green onions, chipotle chili powder, 1 tablespoon lime juice, garlic basil spread, and cumin in a small bowl. Stir until combined; season with salt and black pepper. Cover and refrigerate for at least 1 hour.
Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium heat; cook and stir chorizo, ground beef, and coriander until meat is browned, about 15 minutes. Drain and discard fat. Season with salt and black pepper.
Stir cabbage, green bell pepper, yellow bell pepper, orange bell pepper, jalapeno, and water into chorizo mixture; cook and stir until peppers soften, about 10 minutes. Add brown sugar and chili powder; cook and stir until water is evaporated and sauce is thick, about 10 minutes.
Sprinkle 1/4 cup cilantro and juice of 1 lime over the chorizo mixture and remove from heat.
Spread each hoagie bun with 1 tablespoon chipotle mayo. Evenly distribute the chorizo mixture among the 4 sandwiches.
Heat 1 tablespoon olive oil in a nonstick skillet over medium heat; fry eggs, 2 to 4 at a time if necessary, until whites are set but yolks are still soft, about 2 minutes per side. Place two eggs atop each sandwich.