Combine 2 1/3 cups all-purpose flour, 1 cup vegan margarine, 1 tablespoon white sugar, and salt in a food processor; pulse until mixture clumps together. Pour water in slowly and pulse a few times until a dough forms.

Transfer dough to a flat work surface; knead for 30 seconds and shape into a disk. Wrap with plastic wrap and refrigerate until firm, about 30 minutes.

Preheat the oven to 325 degrees F (165 degrees C).

Dust a flat work surface with flour. Roll dough out into two 10-inch crusts. Press 1 crust gently into a 9-inch pie plate.

Combine brown sugar, 1/2 cup vegan margarine, 1/4 cup white sugar, rice milk, 3 tablespoons flour, cinnamon, and nutmeg in a saucepan; cook and stir over medium heat until margarine melts and brown sugar is dissolved, 3 to 5 minutes.

Place apple slices in a large bowl. Pour brown sugar mixture on top; mix until apples are evenly coated. Pile apples into the bottom crust. Cover with second crust. Cut slits in the top crust with a sharp knife.