Drain the tofu and wrap it in a clean kitchen towel. Place on a cutting board with a sheet pan or board on top and let the tofu drain for 30 minutes. Slice into 1/2-inch thick slices

In a large flat container with a lid, stir together the olive oil, tamari, vinegar, garlic, smoked salt and smoked paprika. Carefully place the tofu slices into the marinade and turn to coat. Marinate for at least an hour or overnight. 

Preheat the grill. While the grill is heating, add the broccoli florets to the marinated tofu and toss to coat. When the grill is hot, swab the hot grill with the vegetable oil.

Drain the tofu and broccoli, reserving the marinade for another batch, if desired. Grill over indirect heat, turning tofu and broccoli often, about every 5 minutes, until the edges of the tofu are starting to brown a bit and the broccoli is crisp-tender.