Prepare the steak marinade up to 24 hours in advance. In a small bowl, combine the garlic, thyme, Spanish paprika and olive oil. Rub the mixture into the bavette steak, wrap in plastic and refrigerate.
Rub corn with a little olive oil and salt. Grill or broil corn until ears are lightly browned. Remove from the grill and allow to cool. Remove the kernels from the cob and place in a large mixing bowl along with the cherry tomatoes, piquillo peppers, scallions, olive oil, vinegar and salt, to taste.
Right before serving the steak, add the mint, basil and parsley leaves and gently toss together. Remove the bavette steak from the refrigerator 45 minutes before cooking. Wipe excess olive oil from steaks, and sprinkle the meat liberally with sea salt. Heat a grill or grill pan to high. Grill the steak until golden brown on both sides and cooked to medium-rare doneness. Let the bavette steak rest for 10 minutes before serving.
To serve, slice the steak against the grain and lay the slices on a platter. Spoon the corn and piquillo salad over the steak and serve.