In a blender or food processor combine 1 cup of the spinach, the mustard, mayonnaise, garlic, salt, and pepper. Cover and blend or process until smooth. Set aside.
Brush one side of each bread slice with oil; place bread, oiled sides down, on waxed paper. Top four of the bread slices with cheese; layer with cucumber, tomato, and the remaining 1 cup spinach. Spread the remaining four bread slices with some of the mayonnaise mixture; set aside the remaining mayonnaise mixture for serving. Place bread slices, spread sides down, on top of vegetables.
In an extra-large skillet cook sandwiches over medium-high heat for 6 to 8 minutes or until bread is toasted, turning once halfway through cooking time. Pass the reserved mayonnaise mixture.