Create the garlic aioli by mincing the garlic. When the garlic is finely minced, sprinkle salt over it. Use the flat part of a large knife to smash the garlic around and form it into a paste. Stir garlic paste into mayo, then stir in lemon juice. Keep refrigerated until ready to use.
Heat a grill pan to medium heat.
Assemble the sandwiches by layering turkey, spinach leaves, fresh slices of tomato that have been lightly salt and peppered, and feta on the bread.
Grill the sandwich on a grill pan or in a panini press until the outside is crisp, and the sandwich is heated through.
Spread the homemade garlic aioli (about 1/2 tablespoon) that you made in step 1 on the top slice of bread.
Cut in half on a diagonal and serve immediately.