For crust: sift flour and salt together into large mixing bowl.
Add chilled coconut oil in spoonfuls and use a pastry cutter or fork to cut the two together until it forms small crumbles.
Add ice cold water, 1 tablespoon at a time and use a wooden spoon to mix. Add only as much water as needed until dough becomes shaggy and holds together when squeezed in your hand.
Gently knead the dough by hand in the bowl and gather any loose scraps. Transfer to a well-floured surface and form into a ball. Divide ball into two and make two disc shaped pieces. Wrap one in plastic for pie tops and place in the fridge.
Lightly flour the top of the dough and a rolling pin and gently roll into a circle shape, about ¼ inch thick. Use a 3.25in diameter shape to cut out circles to be the bottom of the mini pies.
When you have 12 circles cut out, lightly flour and roll out each circle to be a 1.5 times its starting size. Carefully transfer thinned out circles to the muffin tin, using a spatula to prevent tearing. Gently push the dough into the form without creating tears. Try to leave a small lip of dough above the edge of the tin to seal the pie lid. Repeat until all tins have been filled. Refrigerate until apple filling is ready.
Peel and core apples, cutting them into quarters. Using a mandolin, slice apples into thin slices (roughly 1/16th of an inch thick) into a bowl. Squeeze apples to release juices and discard juice.
Add tofu, sugar, arrowroot powder, cinnamon, vanilla, and nutmeg to a food processor and blend until smooth. Pour over apples and stir to combine.
Roll and cut out remaining dough into 3.25 inch diameter circles, 1/8in thick. Remove tin from the refrigerator and top each pie with a crust, sealing the bottom edges with the top edge. Cut a small slit into the top of the pie lid.
Brush pie lids with melted vegan butter and bake for 35 minutes or until golden brown.