01 -
Prepare your grill for indirect cooking, creating a zone of direct high heat and a second zone of indirect heat. For gas grills, preheat for at least 15 minutes. For charcoal, light the charcoal at least 30 minutes prior to grilling.
02 -
Add mayonnaise, basil, lemon zest, garlic, salt, and pepper to a food processor. Process until smooth. Transfer to a serving dish or store in refrigerator for up to 1 week.
03 -
Add olives, giardiniera, and capers to the same food processor (no need to wash). Pulse 3-5 times until ingredients are roughly chopped. Transfer to a serving dish or store in refrigerator for up to 2 weeks.
04 -
Place sausages on the indirect heat side of the grill, as close to the direct heat as possible without being over flame. Close lid and cook for 4-5 minutes. Flip sausages and continue cooking over indirect heat for another 4-5 minutes, until internal temperature reaches 150°F (65°C).
05 -
Transfer sausages to direct heat. Grill 2-3 minutes per side, until well-charred and internal temperature reaches 160°F (71°C). Transfer to a plate to rest briefly.
06 -
Lightly spray brioche rolls with nonstick cooking spray. Place on grill over direct heat for approximately 1 minute until toasted and crisp.
07 -
Place grilled sausage on toasted roll. Top with castelvetrano relish, generous drizzles of lemon basil aioli and balsamic glaze as desired.