Put 3 tablespoons vegetable oil in a large skillet over medium-high heat.
Cut the tofu into 1-inch cubes. Add the tofu to the skillet (it’s okay if the pieces are crowded), sprinkle with salt and pepper, and cook until the bottoms are golden and crisp and release from the pan, about 5 minutes. Use a spatula to stir once they release. Cook, stirring once in a while, to crisp and brown as many sides as possible, another 5 minutes or so.
Trim and halve the cauliflower and cut out the toughest part of the stalk. Break or chop the rest into bite-sized pieces.
Line a plate with towels. When the tofu is ready, transfer it to the towels with a slotted spoon. Add 2 tablespoons oil and the cauliflower to the skillet, sprinkle with salt and pepper, and raise the heat to high. Cook undisturbed until the florets sizzle, about 3 minutes.
Peel and mince 2 cloves garlic.
Stir the cauliflower; let cook undisturbed until lightly browned in places, another 2 to 3 minutes.
Add the garlic to the skillet along with 1 cup ketchup and 1/2 teaspoon cayenne. Cook, stirring, until the ketchup starts to bubble and caramelize around the edges of the skillet.
Return the tofu to the skillet and toss to coat with the sauce; add a splash of water if the mixture needs to be thinner for better coverage.
Turn the heat to medium, cover, and cook until the tofu is warmed through and the cauliflower is tender, 2 to 3 minutes. Taste and adjust the seasoning and serve.