Cut flank steak into 6 equal pieces.
Grind and mix garlic, 2 tablespoons of olive oil, paprika and 1/2 the jalapeño using a mortar and pestle until a paste forms. Rub paste all over flank steak, transfer to resealable plastic bag and refrigerate for 1 hour up to overnight.
In the bottom of a large pot over medium-high heat, add 1 tablespoon olive oil and half the chopped onion and green pepper.
Once onion is translucent, add flank steak and caramelize both sides.
Once flank steak has a crust on both sides, add 8 cups of water, cover and boil for 3 to 4 hours until meat is tender and falling apart.
Remove steak from water and, when cool enough to handle, shred with your hands, removing any extra fat and veins if desired. Reserve and refrigerate stock for soup or other recipes.
In a sauté pan over medium-high heat add the remaining 1 tablespoon olive oil and remaining onion, green pepper and jalapeño. Sauté until onion is translucent.
Add shredded beef and cook until crisp. Season with salt and pepper to taste. Plate each dish with a healthy portion of carne mechada, 1/2 cup of rice, 1/2 cup black beans and a few tajadas.