Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
Prepare the cinnamon apples: Heat a small saucepan over medium heat with the vegan butter or nonstick spray. Once hot, add the apple and season with the cinnamon. Cook for 5 minutes, stirring frequently. Remove from the heat and set aside.
Prepare the sugar cookie dough: In a small bowl, mix the flaxseed meal with the warm water. Set aside for 2 minutes, or until a gel forms, to make flax eggs. In a medium-sized bowl, use a fork to mix together the melted vegan butter, cane sugar, flax eggs, almond milk, vanilla, baking powder and salt. Add the flour and mix until a cookie dough forms. Fold in the cinnamon apples.
Use your hands to roll about a tablespoon (20 g) of cookie dough into a ball. Place the ball on the prepared cookie sheet. Repeat until the baking sheet is full, spacing the balls about 11⁄2 inches (4 cm) apart. You should have about 20 dough balls.
Bake for 9 to 11 minutes, or until the cookies are golden on the edges and they lift easily off the parchment paper.
While the cookies bake, prepare the vanilla icing: In a medium-sized bowl, combine the confectioners’ sugar, almond milk and vanilla, and beat with a whisk or electric mixer until smooth.
Remove the cookies from the oven and allow them to cool before drizzling the icing over them and serving.