Using the whisk attachment, whisk together flours and xanthan gum in mixer for about 3 minutes. Add baking soda, salt, shredded coconut, and sugar and mix briefly. Remove and set aside.
In another mixing bowl, mix together wet ingredients: oil, coconut milk, water, apple cider vinegar, and vanilla extract.
Slowly add flour mixture and mix thoroughly, at least 5 minutes at medium-high speed. (This is needed to get the xanthan gum to work its magic.)
Grease muffin pans liberally. If using muffin liners, spray the inside of the paper cups liberally as well! Fill muffin wells only ⅔ full.
Bake in the oven 30 to 40 minutes, or until a tester comes out clean. Cool completely.
For the strawberry filling: In a small pot, cook the frozen berries over medium-low heat. In a separate bowl, combine cornstarch and sugar. When the berries are warm but not hot, add in the cornstarch mixture to the pot. Cook, stirring frequently, until the mixture is thick, bubbly, and translucent. Remove from heat and mix in margarine and lemon juice. Chill in refrigerator.
For the coconut whipped topping: In a small saucepan, whisk together the agar, cornstarch, sugar, and salt. Whisk in the coconut milk. Over medium heat, bring to a boil, stirring constantly. Lower heat, continue stirring constantly, and simmer for 5 minutes. Remove from heat, and stir in vanilla extract and coconut oil. Immediately pour through a fine mesh strainer to remove any agar bits and place in the refrigerator to chill overnight. Remove from the refrigerator and transfer to a mixer. Whip the mixture until smooth and fluffy.
To assemble: Cut a cone-shaped plug out of the top of each cupcake. Pipe coconut whipped topping around the hole. Pipe fill strawberry filling into the well of the hole until it’s level with the whipped topping.
Tip: Use a piping bag with the big round tip for the strawberry filling for an easier assembly.