Heat oil in a medium saucepan over medium heat. Add cilantro, garlic, chile and basil; sauté 10 seconds. Transfer mixture to blender and let cool. Add vinegar and lime juice. Blend just 10 seconds, so it is chopped but not blended smooth. Transfer mojo to a medium bowl and season with salt and pepper. It is better if prepared 1 day in advance. Cover and place in refrigerator. Bring to room temperature and stir before using.
Take a large sheet of aluminum foil and grease it with olive oil. Put the panela cheese on top and grill it for about 6 minutes, carefully turn it over and roast it for 6 more minutes.
After 12 minutes, carefully remove the cheese from the grill and place it on a plate without the foil. Drizzle cheese with some cilantro mojo. Place remaining mojo in a small bowl and serve with corn tostadas, crackers or warm corn tortillas. Enjoy!