Coarsely chop nuts in processor. Add next 6 ingredients. Blend until mixture forms coarse paste. (This can be made 3 days ahead.) Cover and chill. Let stand at room temperature 1 hour before using.
Divide almond paste among half of bread slices; spread to cover. Top with cheese. Sprinkle with pepper. Cover with remaining bread slices. Brush tops with oil.
Heat 2 large nonstick skillets over medium-high heat. Add 3 sandwiches, oiled side down, to each skillet. Cook until bread is crusty on bottom, about 6 minutes. Brush tops with oil. Turn sandwiches over. Cook until brown and crusty on bottom, pressing to compact, about 6 minutes.