Preheat oven to 350°F. Grease 7 inch springform pan or line with parchment paper.
In large bowl, combine almond flour, cornstarch, olive oil, vegan butter, maple syrup, vanilla bean paste, almond extract, baking soda, baking powder, and salt. Mix until thick, even dough forms.
Press dough evenly into prepared pan. Bake 18 to 22 minutes, until lightly golden on top and set at the edges. Remove from oven and let cool completely in pan, at least 45 minutes to 1 hour.
For frosting, in medium bowl, whip cream cheese, salt, and vanilla bean paste with a hand mixer for 2 to 3 minutes, until light and fluffy.
For compote, combine apples, cinnamon, and lemon juice in small saucepan. Cover and cook over medium-low heat 4 to 5 minutes, until apples release a bit of their own juices and begin to soften at the edges. Uncover and continue cooking 4 to 6 minutes, stirring occasionally, until liquid has mostly reduced and mixture looks glossy and jammy. Apples should hold their shape with a slight bite. Let cool completely.
Once cake is completely cool, spread frosting evenly over top. Spoon apple compote over frosting just before serving, letting it pool slightly in centre.
