Whisk the coconut milk, soy sauce, chili-garlic sauce, ginger, brown sugar and a pinch each of salt and pepper in a small bowl. Firmly press the tofu dry with paper towels, cut into eight 1/2-inch-thick slabs, then firmly press dry again. Arrange in a small baking dish and pour half of the coconut milk mixture over the top; turn to coat. Refrigerate 30 minutes to 1 hour.
Meanwhile, whisk the peanut butter and vinegar into the remaining coconut milk mixture until smooth; season with salt and pepper and set aside for serving.
Preheat a grill to medium high. Oil the grates. Trim the broccoli and peel the stalks; slice into thin spears. Toss with the vegetable oil; season with salt.
Grill the broccoli, turning occasionally, until lightly charred and crisp-tender, 10 to 15 minutes. Remove the tofu from the marinade and pat dry; season with salt. Grill the tofu, lightly brushing occasionally with the marinade, until well marked, about 2 minutes per side. Serve the tofu and broccoli with the peanut sauce. Sprinkle with sesame seeds.