Preheat the oven to 450°F. Wash and dry the fresh produce. Medium dice the potatoes. Quarter the radishes lengthwise. Peel the carrots; halve lengthwise, then cut crosswise into 2-inch pieces. In a bowl, combine the soy glaze and as much of the gochujang as you'd like, depending on how spicy you'd like the dish to be. Pick the mint leaves off the stems.

Line a sheet pan with foil. Coat the center of the foil with a drizzle of olive oil. Pat the pork dry with paper towels; place in a bowl. Add half the glaze; season with salt and pepper. Turn to coat. Transfer to the sheet pan. Roast 20 to 26 minutes for medium (the center may still be slightly pink), or until browned and cooked to your desired degree of doneness. Transfer to a cutting board; let rest at least 5 minutes.

Meanwhile, line a separate sheet pan with foil. Transfer the diced potatoes, quartered radishes, and carrot pieces to the foil. Drizzle with the sesame oil; season with salt and pepper. Toss to coat. Arrange in an even layer. Roast 20 to 24 minutes, or until browned and tender when pierced with a fork. Transfer to a bowl.

To the bowl of roasted vegetables, add the mirin and sesame seeds; toss to coat. Taste, then season with salt and pepper if desired. Find the lines of muscle (or grain) on the rested pork; thinly slice crosswise against the grain. Serve the sliced pork with the finished vegetables. Top the pork with the remaining glaze. Garnish with the mint leaves (tearing just before adding). Enjoy!