Wash the cucumber thoroughly under cool running water and pat it completely dry with a clean kitchen towel or paper towel.
Place the cucumber on a cutting board and slice it into thin matchstick-sized strips that will fit easily inside the roll-ups.
Lay all 8 turkey slices flat on a clean cutting board or work surface, arranging them in a single layer for easy assembly.
If the turkey slices are small, slightly overlap two slices together to create larger roll-ups that hold the filling more securely.
Allow the cream cheese to soften at room temperature for several minutes, then spread a thin, even layer over each turkey slice using the back of a spoon or a butter knife.
Cut each slice of cheddar cheese in half and place one piece on top of each turkey slice, positioning it near the center.
Add several cucumber strips on top of the cheese, keeping the vegetables centered so they remain inside the roll-up when rolled.
If using lettuce or mustard, add a small amount at this stage, being careful not to overfill the turkey slices.
Starting from one end, carefully roll each turkey slice tightly around the cheese and cucumber filling until a compact roll-up forms.
Place the completed roll-ups seam-side down on a serving plate or tray to help them maintain their shape.
Sprinkle the tops with everything bagel seasoning for extra flavor and texture.
Serve immediately or refrigerate for 15 to 20 minutes before serving for a firmer texture and enhanced flavor.