Season tomatoes on both sides with 1 tsp. kosher salt and ½ tsp. black pepper. Drizzle with 1 tbsp. oil. Set aside.
In a medium bowl, mix goat cheese, cream, lemon zest, agave, red pepper flakes, and remaining 1 tbsp. oil, 1 1/2 tsp. kosher salt, and 1/4 tsp. black pepper until well combined. Spread on a platter or plate.
Preheat a gas grill to high; clean and oil grates. Grill tomatoes until well-charred but not overly soft, 2 to 3 minutes per side.
Arrange tomatoes over goat cheese mixture. Drizzle with oil, then top with basil, sea salt, if using, and red pepper flakes.