Heat olive oil in a skillet over medium heat. Season the salmon with salt and pepper and pan-sear for 2-3 minutes per side, depending on thickness, until just cooked through. Remove from heat and let cool.
Mix mayonnaise, grated ginger, grated garlic, lime zest, and lime juice. Use a microplane grater for best results or finely mince the ingredients. Stir until smooth.
Blend soy sauce, brown sugar, sesame oil, and sriracha in a measuring cup. Mix well and divide evenly among 4 small dipping bowls.
Cut cucumber into 2½ inch (6cm) sticks. Julienne the carrot or shred it. Slice green onions into 5-inch (13cm) pieces, halving thicker white parts lengthwise.
Dip each rice paper wrapper in water for 5 seconds until pliable. Place spinach, prepared vegetables, cilantro, and pieces of salmon on the wrapper. Roll tightly.
Cut each roll in half diagonally. Serve with the prepared dipping sauce.