In a large bowl whisk together the eggs, agave, sour cream, oil, lime zest, vanilla and almond extract until completely smooth and blended. Add in the almond flour, arrowroot starch, coconut flour, baking powder, baking soda and sea salt and whisk until smooth. Cover and let sit for at least 30 minutes.

Preheat the oven to 350 F (177 C) and place a rack is in the center of the oven. Line a standard cupcake pan with muffin liners. Fill the muffin cups until just 3/4 full. Gently tap the tin on the counter several times to release any trapped air bubbles.

Bake for 18 minutes on the center rack of the oven. The cupcakes are done when gently pressed on the top and they spring back. Allow the cupcakes to cool in the tin for 20 minutes and then transfer to a rack to finish cooling.

To make the buttercream add the strawberries and agave to a small saucepan over medium heat and cook until the berries release their liquid, smashing the berries with a wooden spoon. This should take about 3-4 minutes. Turn off the heat, add in the basil and let the mixture cool completely. Strain the juice from the agave-strawberry mixture and discard the remaining pulp.

In an electric stand mixer fitted with the paddle attachment add the butter and sugar and mix on low until a paste forms. Drizzled in the cooled berry liquid, turn the mixer to medium speed and continue to beat until the buttercream is well combined and smooth, about 3 minutes more. Smear the frosting over the tops of the cooled cupcakes. I used a star tip for mine.