For charcoal, ignite a full chimney of mesquite hardwood charcoal on firegrate of a charcoal grill. Spread level and set cooking grate in place. For gas, heat a gas grill to high (at least 550°).
Heat a large cast-iron skillet on cooking grate 10 minutes.
Pour oil into pan and tip to coat. Add tomatoes and squash blossoms. Stir quickly, then cook, covered, stirring twice more, until lightly charred, 1 to 1 1/2 minutes. Sprinkle with salt and pepper. With a slotted spoon, transfer vegetables to a platter. Serve with Aioli.