Preheat oven to 400 degrees. Arrange eggplant cut side up on a baking sheet. Make slits in eggplant and insert garlic and thyme. Drizzle with 2 tablespoons oil. Season with 1/2 teaspoon salt. Bake until tender, about 1 hour. Remove from oven; let stand until cool, about 20 minutes.
Scoop flesh into a food processor. Add herbs, 2 tablespoons oil, and lemon juice. Puree until smooth. Pulse with 1 teaspoon salt and pepper to combine. Will keep refrigerated up to 3 days. Serve with crackers or crostini.