In a small bowl, combine the softened cream cheese, mayonnaise, Dijon mustard, and garlic powder, stirring until smooth and well blended. Season with salt and freshly cracked black pepper to taste. While the spread comes together, prepare your vegetables: peel the cucumber and slice it into thin matchsticks, and roughly chop or leave the baby spinach as is. I like to prep my vegetables first so they're ready to go when I need them—this prevents the tortillas from sitting around getting soggy while I'm still cutting.
Lay out one tortilla on a clean, flat surface. Spread approximately 2-3 tablespoons of the cream cheese mixture evenly across the tortilla, leaving a small border at the edges to prevent overflow when rolling. Layer 2-3 slices of turkey breast across the spread, followed by 2 slices of cheddar or Swiss cheese (you can tear them slightly to fit), a generous handful of fresh spinach, and a small handful of cucumber matchsticks. Repeat this assembly process with the remaining three tortillas and fillings. I find it helpful to slightly overlap the fillings rather than spreading them too thick—this keeps them from falling out when slicing and makes the final pinwheels look more professional.
Starting from one end of the first tortilla, roll it tightly toward yourself, using gentle but firm pressure to keep the fillings from bulging out the sides—the key is a snug roll without squeezing so hard that the filling spills out the ends. Once rolled, place it seam-side down on a cutting board. Repeat with the remaining three tortillas. Using a sharp knife, slice each tortilla roll into 1-inch thick pieces, wiping the knife clean between cuts for cleaner edges. You should get approximately 10 pinwheels from each tortilla roll.
Arrange the pinwheels on a serving platter with the spiral side facing up to showcase the colorful layers. Serve immediately at room temperature, or refrigerate for up to 4 hours and serve chilled. These pinwheels are perfect for appetizers, lunch boxes, or as part of a party spread.