Combine cream cheese, Double Gloucester or cheddar, heavy cream, and salt in food processor. Blend until smooth. Set aside.
Combine mayonnaise, garlic, and salt in small bowl and stir until blended. Set aside.
Lay out artisan bread slices on parchment paper or large cutting board.
Place 2 slices of cheddar on 4 of the bread slices. Place 2 slices of provolone on remaining bread slices.
Equally spoon cream cheese spread on slices with provolone. Gently smooth cream cheese spread over each slice.
Press cheddar side and provolone side together.
Heat a large skillet over medium heat for 5 minutes, until hot.
Brush both sides of the sandwiches with garlic spread.
Grill sandwiches for 2 minutes on each side, until cheese is melted and bread is golden brown.
