Melt butter in a wide skillet over medium heat. Add brown sugar and stir well, breaking up clumps. Let mixture simmer until sugar has mostly dissolved, about 5 minutes. Raise heat to medium-high, stir in apples, salt, and cinnamon, and cook, stirring occasionally, until apples are tender but not mushy, about 8 minutes. The sugar will seize up but will melt into the liquid that the apples release as they cook. Transfer mixture to a bowl and let it cool completely.
Do Ahead: You can keep the filling in the fridge for up to 3 days.
Work with one roti at a time, keeping it between the plastic squares it comes in (roti is very sticky) and keeping the others in the fridge as you form each pie. Put a roti on a work surface. Use your palm to stretch roti slightly, starting in the center and applying gentle pressure as you move toward the edges.
Peel off top layer of plastic. Stir filling, then add 3 Tbsp.–¼ cup (depending on diameter of roti) of filling to the center of the roti. Holding two corners of the remaining plastic square, fold roti over filling to form a semicircle, gently forcing air out but keeping filling in. Firmly press rounded edge of roti to create a seal, then crimp with a fork. Use a sharp knife to make three slashes on the top (so it doesn’t burst), cutting through roti layer and leaving ½" or so between slashes. Sprinkle some sugar (about 1 tsp.) on top, then fold plastic over and use your hands to gently press so sugar adheres. Do the same on the other side of the pie.
Repeat with remaining roti and filling. Chill pies in the fridge for at least 30 minutes before frying.
Do Ahead: You can keep the pies covered in the fridge for up to 12 hours, or freeze them—first uncovered on a plate, then in bags with parchment paper in between the pies—for up to 3 months.
Preheat oven to 200°F and set a rack over a baking sheet. Pour enough oil into a large pot to reach a depth of about 3". Set pot over medium-high heat and bring oil to 350°F (use a deep-fry thermometer). Fry pies 4 or so at a time, carefully turning them over halfway through if they float to the surface, until golden brown and crispy, 3–4 minutes per batch. (If you're frying frozen pies, they'll take about 6 minutes.)
Transfer them to rack and keep them warm in oven. Let oil come back to 350°F between batches. Let them cool slightly before you eat.
