Place an oven rack in the center of the oven; preheat to 450°F. Drain the tofu, then place on a paper towel-lined plate. Place several layers of paper towels on top, then place a heavy-bottomed pot (or pan) on top of the paper towels. Set aside to release the excess liquid at least 10 minutes.

Meanwhile, wash and dry the fresh produce. Cut off and discard the bottom 1/2 inch of the broccoli stem; cut the broccoli into small florets. Quarter the lime. Small dice the cucumber. Cut off and discard the stem of the pepper. Halve lengthwise; remove the ribs and seeds, then small dice. In a bowl, combine the diced cucumber, diced pepper, mirin, and a drizzle of olive oil. Season with salt and pepper. Set aside to marinate, stirring occasionally, at least 10 minutes. In a separate bowl, combine the mayonnaise and soy glaze.

Carefully rinse the rice (sifting through for any impurities). Drain thoroughly. In a medium pot, combine the rice, a big pinch of salt, and 3/4 cup of water (or 1 1/2 cups for 4 servings). Heat to boiling on high. Once boiling, reduce the heat to low. Cover and cook, without stirring, 15 to 17 minutes, or until the water has been absorbed and the rice is tender. Turn off the heat and fluff with a fork.

Meanwhile, place the broccoli florets on a sheet pan. Drizzle with olive oil and season with salt and pepper. Toss to coat and arrange in an even layer. Roast 14 to 16 minutes, or until browned and tender when pierced with a fork. Remove from the oven. Top with the juice of 2 lime wedges and carefully stir to coat.

Meanwhile, transfer the pressed tofu to a cutting board. Cut the tofu in half horizontally, then halve each piece crosswise. Season with salt and pepper on both sides. Crack the egg into a bowl; add the soy sauce and beat until smooth. Place the flour and breadcrumbs on two separate large plates. Season each with salt and pepper. Season the breadcrumbs with all but a pinch of the togarashi. Working one piece at a time, thoroughly coat the seasoned tofu in the seasoned flour (tapping off any excess), then in the egg-soy sauce mixture (letting any excess drip off), then in the seasoned breadcrumbs (pressing gently to adhere). Transfer to a separate plate.

In a large pan (nonstick, if you have one), heat a thin layer of oil on medium-high. Once the oil is hot enough that a pinch of breadcrumbs sizzles immediately when added, add the coated tofu in an even layer. Cook 3 to 4 minutes per side (if the pan seems dry, add a drizzle of oil before flipping), or until golden brown and crispy. Transfer to a paper towel-lined plate and immediately season with salt. Serve the cooked rice topped with the cooked tofu, roasted broccoli, and marinated vegetables (including any liquid). Drizzle the tofu with the soy mayo. Garnish with the remaining togarashi. Serve the remaining lime wedges on the side. Enjoy!