Add chopped strawberries to a medium pot, cover, and heat over medium until simmering, about 5 minutes.
Reduce heat to low, uncovered, stirring frequently and simmer until mixture reduces by half, about 20-30 minutes.
Cool slightly then blend the mixture to a thick puree. Reserve 1/3 cup for the cake, refrigerate the rest for buttercream.
Preheat oven to 350°F. Grease an 8x2 inch round cake pan and line the bottom with parchment paper.
Whisk almond flour, baking powder, and salt together in a medium bowl.
In a large bowl, whisk eggs, strawberry puree, cane sugar, olive oil, and vanilla extract.
Fold dry ingredients gently into wet ingredients until just combined, avoiding over mixing.
Pour batter into prepared pan and spread evenly with an offset spatula.
Bake for 25 to 27 minutes or until a toothpick inserted in the center comes out clean.
Cool cake in pan for 10 minutes, then transfer to a wire rack to cool completely.
Beat vegan butter, powdered sugar, and vanilla with an electric mixer starting on low then medium-high for 3-5 minutes until fluffy.
Slowly mix in reserved strawberry puree until frosting is creamy and evenly blended.
Spread buttercream evenly over completely cooled cake and garnish with extra strawberries if desired.