Mix the chopped peaches, brown sugar, nutmeg, lime juice, and tapioca starch in a bowl. Allow the mixture to rest for about 10 minutes.
Place a spring roll wrapper on a flat surface with one corner facing you. Spoon approximately 2 tablespoons of the peach filling into the center.
Fold the bottom corner over the filling, tuck in the sides, and roll it up tightly, sealing the top edge with a dab of water.
Heat the coconut oil in a deep pan over medium-high heat. Once shimmering, add the spring rolls in batches, frying until golden and crispy (about 3-4 minutes per side).
Transfer the fried spring rolls to a plate lined with paper towels to absorb excess oil.
While warm, sprinkle the spring rolls generously with cinnamon sugar and serve hot, garnished with fresh mint leaves if desired.