Drain tofu, then cut block in half crosswise. Cut each half into 1" pieces. Poke each piece with a fork. Arrange in a 9" x 9" baking dish in a single layer.

Peel and smash 2 garlic cloves and transfer to a small saucepan. Add water, 2 Tbsp. salt, 1/2 tsp. oregano, and 1/2 tsp. red pepper flakes and bring to a boil over high heat. Pour brine over tofu. Let sit 20 minutes.

Line a baking sheet with paper towels or a clean kitchen towel. Working one or two at a time, remove tofu from brine and pat dry on all sides with more paper towels. Arrange on prepared sheet. Cover with more paper towels or another clean kitchen towel and lightly pat dry again (do not apply too much pressure).

In a shallow bowl, combine cornstarch, onion powder, paprika, 1/2 tsp. oregano, 1/2 tsp. red pepper flakes, and a pinch of salt. Transfer tofu to bowl and gently toss to coat in cornstarch mixture. Discard paper towels. Set a wire rack over same baking sheet.

In a large nonstick skillet over medium-high heat, heat oil. Add tofu and cook, turning occasionally, until browned on all sides, about 10 minutes. Transfer to prepared rack; season with salt. Wipe out skillet.

Finely chop remaining 2 garlic cloves. In same skillet over medium heat, melt butter. Add chopped garlic and remaining 1/4 tsp. oregano and pinch of red pepper flakes. Cook, stirring, until fragrant, about 30 seconds. Add tomato paste and cook, stirring, until paste is brick-red, about 30 seconds more. Add cream, tomatoes, and Parmesan. Cook, stirring, until cheese is melted, about 2 minutes.

Add tofu and basil to skillet and cook, stirring, until warmed through, about 30 seconds; season with salt and black pepper. Add more cream, 1 Tbsp. at a time, if sauce is too thick. Top with more basil and Parmesan.