Tofu Katsu Curry

Make curry roux: In a small saucepan, heat 2 tablespoons olive oil over medium heat. Add flour gradually, whisking to combine. Continue cooking, whisking constantly, until golden and fragrant, 1 to 2 minutes. Stir in spices and cook, stirring, until very fragrant, 30 seconds to 1 minute. (Mixture should be texture of wet sand.)  Carefully transfer to a small bowl while you prepare vegetables. Sauté mushrooms: In a large skillet over medium heat, heat 1 tablespoon olive oil. Add mushrooms and arrange in a single layer, cut side down. Cook undisturbed until cut sides are golden, about 4 minutes. Stir, season with salt, and cook 3 to 4 minutes more. Remove from heat. Cut onion in half root to tip then cut each half into 4 thick slices, removing tip and root. Heat remaining tablespoon olive oil in a large pot over medium heat. Add onion, season with salt, and cook, stirring occasionally, until onions have softened slightly and are turning golden at edges, 4 minutes. Add ginger and cook until fragrant, 1 minute more. To onions, add broth and a big pinch of salt. Bring to a boil, scraping up any brown bits with a wooden spoon. Reduce heat to a simmer.  Transfer about 1/2 cup cooking liquid to a small bowl and whisk in about a quarter of the curry roux. Return mixture to pot and stir to combine. Repeat 3 more times until all of the roux is dissolved into the pot. Add potato and simmer, partially covered, about 5 minutes. Add carrots and half the grated apple. (The vegetables should just be covered with liquid; add more water as necessary.) Return to a simmer and cook, partially covered, until carrots and potatoes are just tender, 8 to 10 minutes.  Stir in cooked mushrooms, tomatoes, and remaining apple then season to taste with soy sauce. On a cutting board, sandwich tofu between doubled layers of paper towels and press down slowly with a flat-bottomed pan or second cutting board to remove moisture without cracking block. Discard paper towel and stand tofu up on its short, small side. Cut tofu into thirds, into 3 thinner rectangles. Season each slice on all sides with salt. Make breading station: Add flour to one shallow bowl, nondairy milk to another shallow bowl, and panko to a third. Whisk mustard into bowl with milk and sesame seeds into bowl with panko. Line a baking sheet with paper towels and fit with a rack. Work with one piece of tofu at a time, dredge tofu in flour, shaking off excess. Add the tofu to the milk mixture, then return it to the flour. Dip back in the milk, and finally into the panko mixture, pressing with your fingers to help crumbs adhere. Transfer breaded tofu to prepared rack and repeat with remaining pieces. Heat about ½ inch vegetable oil in a large skillet over medium-high heat. The oil is ready when a piece of panko bubbles immediately when added to oil. Add the tofu to the hot oil and cook until golden on underside, 4 to 6 minutes. Flip and cook until golden on other side, 4 to 6 minutes more. Transfer to cooling rack and season with salt. Serve tofu, sliced, over rice and curry.