In a medium bowl, combine the softened cream cheese and garlic powder, stirring until smooth and well blended. Fold in the shredded cheddar cheese, sweet pickle relish, and green onions until everything is evenly distributed. The mixture should be spreadable but hold its shape. I prefer to use freshly shredded cheddar here rather than pre-shredded, as it melts more smoothly into the cream cheese and creates a better texture for spreading.

Lay out one flour tortilla on a clean work surface. Spread about 1/4 of the filling mixture from Step 1 evenly across the tortilla, leaving a small 1/2-inch border around all edges to prevent the filling from squishing out when you roll. Layer 2-3 slices of thinly sliced deli ham directly over the filling, then tightly roll the tortilla away from you into a cylinder, pressing gently as you go to create a compact roll. Repeat with the remaining three tortillas and filling. Wrap each roll individually in plastic wrap and refrigerate for 4 to 8 hours—this chilling time allows the filling to set and makes slicing clean and easy.

Remove the chilled rolls from the refrigerator and unwrap them. Using a sharp serrated knife, trim about 1/2 inch off each end of every roll to create clean edges, then discard the end pieces. Slice each roll into 8 equal pieces, wiping your knife clean between cuts for neat presentation. I find that dipping the knife in warm water between slices helps the cream cheese cut smoothly without tearing or dragging. Arrange the pinwheels on a serving platter and serve cold or at room temperature.