Towel-wrap tofu; press under moderately heavy plate 25 minutes. Heat oven to 425°F; line 18-by-13-inch rimmed sheet with parchment rated for temperature.
Cut tofu into 1-inch cubes; pat dry. Toss with 1 tablespoon oil, cornstarch, paprika, and 1/4 teaspoon salt. Spread over half pan.
Roast tofu 15 minutes. Toss broccoli and onion with remaining oil and salt and pepper; add to other half. Turn tofu.
Roast 15 minutes more until tofu corners firm and broccoli edges browned. Mix barbecue sauce and vinegar.
Lightly sauce tofu; roast 5 to 7 minutes more until tacky. Divide tofu and vegetables among 3 plates.