Fill a medium pot (or large for 4 servings) 3/4 of the way up with salted water; cover and heat to boiling on high. Wash and dry the fresh produce. Thinly slice the mushrooms. Peel the ginger; finely chop to get 2 teaspoons (or 4 teaspoons for 4 servings). Thinly slice the scallions, separating the white bottoms and hollow green tops. Halve the snow peas crosswise (removing the tough strings if desired). Thinly slice the cucumbers into rounds. In a bowl, combine the sliced cucumbers and vinegar; season with salt and pepper. Set aside to marinate, stirring occasionally. To make the sauce, melt the butter in a large bowl in the microwave (or melt in a small pot on the stove, then transfer to a large bowl). Add the miso paste, soy-miso sauce, and 1 tablespoon of water (or 2 tablespoons for 4 servings); whisk to combine. To make the glaze, in a separate bowl, whisk together the honey, 1 tablespoon of water (or 2 tablespoons for 4 servings), and as much of the gochujang as you'd like, depending on how spicy you'd like the dish to be.

Meanwhile, in a medium nonstick pan (or large for 4 servings), heat a drizzle of olive oil on medium-high until hot. Add the sliced mushrooms in an even layer. Cook, without stirring, 3 to 4 minutes, or until browned. Add the chopped ginger, sliced white bottoms of the scallions, and halved peas; season with salt and pepper. Cook, stirring occasionally, 2 to 3 minutes, or until softened. Transfer to the bowl of miso-butter sauce; stir to coat. Wipe out the pan.

Add the noodles to the same pot of boiling water, stirring gently to separate. Cook, stirring occasionally, 3 to 5 minutes, or until tender. Turn off the heat. Drain thoroughly and rinse under warm water 30 seconds to 1 minute to prevent sticking. Transfer to the bowl of cooked vegetables and sauce. Toss to combine. Taste, then season with salt and pepper if desired.

Meanwhile, pat the pork belly dry with paper towels. Place on a cutting board with the fat cap facing up; cut crosswise into 1/2-inch-thick pieces. Heat the same pan on medium- high until hot. Add the pork belly pieces in an even layer. Cook 4 to 6 minutes, or until browned. Flip and cook 3 to 5 minutes, or until browned and heated through. Transfer to a paper towel-lined plate. Carefully drain off and discard any excess fat. 

*The USDA recommends reheating cooked pork to 140°F.

Heat the same pan on medium-high until hot. Add the browned pork belly and gochujang glaze (carefully, as the liquid may splatter). Cook, stirring frequently, 30 seconds to 1 minute, or until thickened and the pork is coated. Turn off the heat. Halve the peeled eggs lengthwise; season with salt and pepper. Serve the finished noodles topped with the glazed pork belly, marinated cucumbers, and seasoned eggs. Garnish with the sliced green tops of the scallions and as much of the togarashi as you'd like. Enjoy!