How to Make It
Heat 1 tablespoon oil in a small saucepan over medium. Add shallot and mustard seeds; cook, stirring occasionally, until seeds begin to pop, about 1 minute. Add sugar, vinegar, and ¼ cup water; cook, stirring occasionally, until sugar dissolves, about 1 minute. Add plums; cook, stirring often, until mixture is thickened and plums are soft, about 6 minutes. Stir in ¾ teaspoon kosher salt. Transfer to a bowl, cover, and refrigerate until ready to serve. (Mostarda can be made and refrigerated up to 3 days in advance.)
Rub lamb all over with 2 tablespoons oil; season with thyme, black pepper, and 4 teaspoons kosher salt. Let rest at room temperature for at least 30 minutes and up to 1 hour. (Lamb can be seasoned and refrigerated up to 1 day in advance. Bring to room temperature before grilling.)
Prepare grill for medium-high in direct heat. Place lamb over direct heat and grill, uncovered, flipping once, until charred in spots and grill marks appear, about 8 minutes per side.
Move lamb to indirect heat. Place a large cast-iron skillet over direct heat. Grill lamb, covered, until a thermometer inserted in thickest portion registers 140°F for medium, 10 to 12 minutes. Transfer to a cutting board; let rest for 15 minutes before slicing.
Toss shishitos with remaining 2 tablespoons oil. Add to skillet and cook, tossing, until blistered in spots, 6 to 8 minutes. Season with remaining ½ teaspoon kosher salt.
Season lamb with flaky salt and black pepper. Serve with shishitos and mostarda.