Add all listed ingredients to a food processor. Season with 1/2 teaspoon kosher salt & ground black pepper as desired. Pulse to combine. Taste & season with additional salt or ground black pepper as needed. Set aside for serving, or store in an airtight container in the refrigerator for up to 1 week.
Place the mushroom caps on a small baking sheet. Because mushrooms are so absorptive, it’s best to prep them right before grilling. Brush the entire surface of the mushroom caps with avocado oil, enough to nicely coat both sides of the mushrooms, then season generously with about 1 1/2 teaspoons kosher salt & ground black pepper as desired.
Place the portobello mushroom caps on the grill grates. Close the grill lid & grill the mushrooms 4-5 minutes per side, until they are as tender & charred as desired. Transfer to a small baking sheet or plate.