Season both sides of the sliced tofu with salt and pepper.
In a shallow bowl, whisk together the flour and 2 tablespoons of cornstarch.
Dredge the tofu lightly, shaking off any excess coating. Set aside.
Heat olive oil in a large skillet over medium heat.
Add 1 tablespoon of butter and let it melt.
Add the tofu in a single layer and cook, undisturbed, until deeply golden and easily releases from the skillet, about 4 to 5 minutes per side.
Transfer to a paper towel-lined plate.
Reduce the heat to medium-low and add the remaining 1.5 tablespoons of vegan butter to the same pan.
Add the shallot and cook until softened and fragrant, about 2 minutes.
Add the garlic and cook for about 30 seconds, just until aromatic.
Stir in the broth, lemon juice, and lemon zest, scraping up the browned bits from the bottom of the pan.
Bring the sauce to a simmer and cook for 4 to 6 minutes, until slightly reduced.
In a small bowl, combine the remaining ½ teaspoon cornstarch with 1 tablespoon water to make a slurry.
Stir it into the sauce and cook for 1 to 2 minutes, until lightly thickened.
Stir in the capers.
Return the tofu to the skillet and sprinkle in the parsley.
Spoon the sauce over the tofu and simmer gently for 2 to 3 minutes, just until warmed through and slightly infused with the sauce.
Taste and adjust with additional salt, pepper, or lemon juice as needed.
Serve hot, spooning extra sauce over each portion.
