In a shallow bowl, whisk together the tahini and water until you have a smooth, creamy mixture.
Season generously with salt and pepper.
Place the panko breadcrumbs in a second shallow bowl.
Heat 2 tablespoons (30 ml / 1 fl oz) of the olive oil in a large skillet over medium-high heat.
Season the tofu slices with salt and pepper.
Dip each slice first into the tahini mixture, ensuring it's lightly coated, then press it firmly into the panko crumbs, covering both sides completely.
Carefully place the coated tofu in the hot skillet.
Fry for 3-4 minutes per side, until golden brown and crispy.
Work in batches if necessary to avoid overcrowding the pan, adding more oil as needed.
Transfer the cooked tofu to a plate and keep warm.
In the same skillet, heat the remaining 1 tablespoon (15 ml / 0.5 fl oz) of oil over medium heat.
Add the minced shallots and cook until softened and fragrant, about 2 minutes.
Stir in the capers, then pour in the white wine and vegetable broth.
Bring to a simmer and let it cook, scraping up any browned bits from the bottom of the pan, until the sauce has reduced by about a quarter.
Remove the skillet from the heat and stir in the vegan butter, lemon juice, and 2 tablespoons (30 ml / 1 fl oz) of fresh parsley until the butter is melted and the sauce is glossy.
Season with salt and pepper to taste.
To serve, arrange the crispy tofu cutlets on a platter and pour the delicious lemon-caper sauce over the top.
Garnish with a sprinkle of fresh parsley and enjoy immediately!