For the Chicken and Vegetables: Adjust oven rack to upper-middle position. Set an empty rimmed baking sheet on upper-middle rack, and preheat oven with baking sheet to 450°F(230℃). In a small bowl, whisk together gochujang, vinegar, ginger, salt, pepper, and 2 tablespoons of the oil until smooth; set aside.

In a large bowl, toss potatoes, Brussels sprouts, shallots, 2 tablespoons of the prepared gochujang mixture, and the remaining 1 tablespoon oil until evenly coated. Working quickly, carefully spread vegetables in an even layer on preheated baking sheet. Roast on the upper-middle rack in oven until lightly browned on bottom and just beginning to turn tender, about 15 minutes.

Meanwhile, pat chicken thighs dry with paper towels and rub all sides evenly with remaining 2 tablespoons gochujang mixture. Gently flip vegetables over, nestle chicken thighs, skin side up, between vegetables on baking sheet. Make sure chicken and vegetables all have direct contact with the sheet pan and are evenly spaced apart. Sprinkle bacon on top and around vegetables and chicken.

Reduce oven temperature to 400°F (205°C), and bake on upper-middle rack until a thermometer inserted into thickest part of chicken registers 175°F (79 ℃), skin is crispy, bacon is cooked, and vegetables are tender, 25 to 30 minutes.

For the Mayo Gochujang Sauce: While the chicken is cooking, in a small bowl, whisk together mayonnaise, gochujang, rice vinegar, pepper, and salt until smooth. Cover and refrigerate until ready to use.

Sprinkle chicken and vegetables with sesame seeds. Serve with mayo-gochujang sauce.