Cut the avocados in half and remove the seeds. Peel the garlic clove and cut the top off. Rub the cut part of the garlic all over the cut side of the avocado.
Mix the olive oil and lemon juice in a small bowl and brush over the avocados. Sprinkle with salt.
Place cut side down on the grill and cook until nice grill marks form, about 5-6 minutes.
Place the feta into a small microwave-safe bowl and microwave until it begins to warm and soften, about 10-15 seconds. Then, use a small food processor (mine is 3 cups) and blend all the sauce ingredients together. You'll need to stop and scrape down the sides and then start blending again to make sure everything gets smooth and creamy. Season to taste with salt.
Divide the sauce between the avocados, squeeze with fresh lemon juice (optional) and scoop right out of the shell to DEVOUR!