Preheat oven to 350°F. Line two 12-cup muffin pans (24 wells total) with paper liners or spray the wells with nonstick cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, combine the French vanilla cake mix and the instant coconut cream pudding mix.
Add the sour cream, vegetable oil, slightly beaten eggs, and 4 ounces (1/2 cup) of the 13-ounce can of unsweetened coconut milk. Beat on medium speed for about 2 minutes, until the batter is smooth and well combined.
Fold in the 2/3 cup sweetened shredded coconut with a rubber spatula until evenly distributed.
Using a large cookie scoop (or a tablespoon), distribute the batter evenly among the 24 muffin wells — about 3 tablespoons of batter per well.
Bake in the preheated oven for 18–22 minutes, or until the tops spring back when lightly touched and a toothpick inserted in the center comes out clean.
Remove the pans from the oven and let the cupcakes cool in the muffin tins for about 10 minutes. Then transfer the cupcakes to a wire rack to cool completely while you prepare the frosting.
Pour the remaining 9 ounces of unsweetened coconut milk into a medium saucepan with high sides. Over medium heat, bring it to a gentle boil, stirring occasionally to prevent scorching.
Reduce the heat to medium-low and simmer the coconut milk, stirring occasionally, until it reduces and thickens slightly — about 20 minutes. Turn off the heat and let the reduced coconut milk cool completely, then cover and chill in the refrigerator for about 1 hour to thicken.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer and a large bowl), beat the 2 cups room-temperature unsalted butter together with the chilled, reduced coconut milk on medium-high speed for about 5 minutes, until combined and slightly lightened.
Add the lime zest, 1 teaspoon vanilla extract, and 1/2 teaspoon coconut extract; mix briefly to combine.
Turn the mixer to low and gradually add the 1 1/2 pounds confectioners’ sugar, mixing until fully incorporated and the frosting is smooth.
Increase the mixer to medium-high and beat the frosting for 3–4 minutes, until light and fluffy. Taste and adjust texture by adding a little more confectioners’ sugar if too thin, or beating longer if denser is desired.
Pipe or spread the frosting onto the completely cooled cupcakes. If desired, garnish with a light dusting of shredded coconut or additional lime zest.