Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Press the extra firm tofu between paper towels for 15 minutes to remove excess moisture, then cut into uniform 1/2-inch cubes.
On the prepared baking sheet, toss the tofu cubes and cherry tomatoes with the olive oil, minced garlic, sea salt, and black pepper until evenly coated.
Roast for 20 to 25 minutes, tossing halfway through, until the tofu is golden and the tomatoes have softened and burst.
While the vegetables roast, cook the chickpea pasta in a pot of boiling salted water according to the package instructions until al dente, then drain.
Transfer the cooked pasta to a large mixing bowl and add the roasted tofu and tomatoes, making sure to scrape all the juices from the pan into the bowl.
Sprinkle the nutritional yeast over the pasta mixture and toss gently until the yeast forms a light, savory sauce with the tomato juices.
Divide the pasta into serving bowls and place the burrata cheese on top, gently breaking the outer shell to allow the creamy center to spill out.
Finish the dish with a drizzle of balsamic glaze and a generous handful of fresh torn basil leaves.