Heat a gas or charcoal grill so that the temperature is maintaining a steady 375°. If your grill doesn’t have a thermometer, aim for a medium-hot heat.
Remove the pie crust from the refrigerator and allow it to come to room temperature as instructed on the package.
Meanwhile, prepare the fruit for the recipe. Wash the blueberries and let drain on a paper towel. Cut the pineapple into bite-sized pieces. In a medium bowl, combine the prepared blueberries and pineapple with the basil, flour, and one tablespoon of the sugar. Toss everything together so that the fruit is well coated with the flour and sugar.
Unroll the pie crust onto a pan. Brush the surface of the pie crust with half of the melted apple jelly.
Mound the pineapple-blueberry-basil filling in the center of the crust leaving a 2” margin all around. Bring the crust up over the filling creating a freeform, rustic edge.
Beat the egg in a small bowl. Brush all the exposed crust with the beaten egg. Sprinkle the remaining sugar on the egg-washed pie crust.
Place the pan on the indirect heat side of your grill. Close the grill cover and cook for 30-35 minutes or until the crust is nicely browned and the filling is bubbly.
Remove and let stand for 5 minutes before serving. Just before serving, brush the top of the fruit with the remaining melted apple jelly.