First, prepare the lime curd. In a small pot, whisk together the nondairy milk, water, and cornstarch.
Place over medium-high heat and add in the lime juice, lime zest, sugar, and vegan butter, continuing to whisk. Mixture should start bubbling and thickening. Whisk for 1-2 minutes as it boils, then remove from heat. Set curd aside to cool until needed. It has to be COLD before it can be used in the cake.
Next, make the cake. Preheat oven to 350F and spray two 6" round cake pans with nonstick baking spray. In a small bowl, whisk together the ground flaxseed with the water and set aside to thicken.
In the bowl of a stand mixer, combine the flour, baking powder, baking soda, salt, and sugar.
Add in the vegan butter, and beat on low until it's incorporated and has a sandy texture.
In a small bowl, whisk together the oil, flaxseed mixture, nondairy yogurt, lime zest, and add them to the dry ingredients. Mix until combined.
Pour in the unsweetened nondairy milk and lime juice, and beat on medium-low until smooth and creamy. Finally, gently stir in the strawberry pieces.
Divide batter evenly among the 2 pans, and bake for 45 minutes until cake is set in the center and a toothpick comes out clean.
When lime curd and cakes are completely cooled, you can make the frosting. In the bowl of a stand mixer, beat the shortening and vegan butter together until completely smooth and creamy. Add in the powdered sugar, 1 cup at a time, until a thick frosting forms. Add in a few spoonfuls of the lime curd until frosting reaches desired color and flavor. If it gets too runny, just add in a bit more powdered sugar.
To assemble the cake, divide the 2 cake layers in half to create 4 thin layers. Place one cake piece on your cake stand or platter, and pipe a layer of lime frosting on top. Repeat with all.
Frost the outside of the cake as desired, and decorate the top with an open star tip (1M). Finish with halved lime slices and fresh strawberries on top!