Add blackberries, soy sauce, honey, lime juice, olive oil, garlic, thyme, rosemary, and black pepper to a blender. Blend until smooth.
Add marinade to a bag with steak. Seal and place in the refrigerator for 6 to 12 hours. Remove from the refrigerator for 30 minutes before cooking to rest at room temperature.
Preheat the grill to medium-high heat (350˚ to 450˚F). Remove steak from marinade and grill for 6 minutes on one side. Flip and cook for another 5 to 6 minutes, until medium-rare. Cook longer if you prefer for desired doneness.
Place cooked steak on a cutting board and let rest for 10 minutes. Slice against the grain into thin strips.
Stir together salsa ingredients in a small bowl.
To assemble tacos, add steak to tortillas. Top with salsa and queso fresco. Serve.