Pat the tri-tip roast dry with paper towels. In a small bowl, combine smoked paprika, kosher salt, black pepper, garlic powder, onion powder, dried oregano, and cayenne pepper. Drizzle the olive oil over the roast and rub it all over to coat evenly. Apply the spice rub generously on all sides, pressing it firmly into the meat. For best results, refrigerate uncovered for at least 1 hour or overnight.

Preheat your grill for two-zone cooking: heat one side to high (direct heat) and leave the other side off or on low (indirect heat). Target a grill temperature of around 375°F over the indirect zone.

Place the tri-tip fat-cap side up over the indirect heat zone. Close the lid and cook, turning once halfway through, until the internal temperature reaches 110°F for medium-rare or 115°F for medium. This typically takes 25 to 30 minutes depending on thickness.

Move the tri-tip over the direct high-heat zone. Sear for 2 to 3 minutes per side, turning as needed, until a deep, charred crust forms on all surfaces and the internal temperature reaches 125°F for medium-rare or 130°F for medium.

Transfer the tri-tip to a cutting board and tent loosely with aluminum foil. Rest for 10 to 15 minutes — do not skip this step.

Optional butter finish: While the roast rests, melt butter in a small pan with minced garlic and thyme over low heat for 2 minutes. Spoon over the rested roast just before slicing.

Locate the two grain directions on the tri-tip. Cut the roast in half at the center point where the grains meet. Slice each half thinly (about 1/4 inch) against its own grain direction. Arrange on a platter and serve immediately.