ITALIAN SAUSAGE (HOT OR MILD)
NONSTICK COOKING SPRAY
BRIOCHE HOT DOG BUNS
PITTED CASTELVETRANO OLIVES
GIARDINIERA (MILD OR HOT)
KOSHER SALT & GROUND BLACK PEPPER
Prepare your grill for indirect cooking, creating a zone of direct high heat & a second zone of indirect heat. If using a gas grill, begin preheating at least 15 minutes before grilling. If using charcoal, light the charcoal at least 30 minutes prior to grilling.
Add all listed ingredients to a food processor. Process until combined into a smooth mixture. Transfer to a serving dish and set aside, or store in the refrigerator in an airtight container for up to 1 week.
Add all listed ingredients to the same food processor used to make the aioli (no need to even wash it!). Pulse just 3-5 times, just until the olives & giardiniera are roughly chopped. Transfer to a serving dish and set aside, or store in the refrigerator in an airtight container for up to 2 weeks.
Once the grill is hot, place the sausage directly on the indirect heat side of the grill, arranging the sausage as close to the direct heat as possible without being directly over the flame. Close the lid & cook for 4-5 minutes. The heat from the direct heat side of the grill will circulate around the sausage, cooking them with really gentle indirect heat. After 4-5 minutes, flip the sausage, & cook over indirect heat for another 4-5 minutes, or until an instant-read thermometer inserted in the center of the sausage registers a temperature of 150 degrees F.
Transfer the sausage to the direct heat. Grill 2-3 minutes per side, until charred as desired & the internal temperature reaches 160 degrees F. Transfer to a plate to rest & cool slightly before serving.
Lightly spritz the rolls with nonstick cooking spray. Place the rolls on the grill grates over direct heat. Cook for 1 minute or so, until as toasty & crisp as desired.
Serve the grilled sausage on a toasted roll, topped with castelvetrano relish & generous drizzles of lemon basil aioli & balsamic glaze, as desired.