Cakes:
Preheat the oven to 350 F (180 C).
Grease 6 molds of 3 and 1/2 inches (9 cm) in diameter and 2 inches (5 cm) high with cooking spray or lightly oil them.
Wrap the molds with aluminum foil, leaving 1 inch (2 cm) of overhang at the top to prevent spills.

Drain the pineapple by placing it in a strainer and pressing on it with a spoon to extract as much juice as possible.
Pour the flour into a large bowl. Sprinkle with baking powder, baking soda, salt, cinnamon, and nutmeg. Mix well.

Place the butter in a large bowl and beat it with an electric mixer until creamy.
Add the brown sugar and continue beating at medium speed for about 3 minutes.
Add the eggs one at a time, followed by the vanilla extract.
With the mixer on low speed, add about one-third of the flour mixture and mix until just combined, then add half of the milk.
Repeat the sequence, ending with the flour mixture. The batter will be very thick.
Gradually add the crushed pineapple and grated carrots.

Divide the batter among the molds. Smooth the top to the edges of the mold.
To eliminate air pockets, tap the molds 5 or 6 times on the counter.
Bake for 30-35 minutes or until the center of the cake feels firm to the touch.
Let the cakes cool in their molds on a wire rack.
Unmold the cakes after about 15 minutes and let them cool completely on a wire rack.
It’s best to bake the cakes a day before frosting and refrigerating them overnight.

Frosting: Cut the cream cheese into small pieces.
Place the butter in a bowl and beat it with an electric mixer until creamy.
Add the sour cream and vanilla extract, beating continuously.
Reduce the mixer speed to low and incorporate the cream cheese, one piece at a time.
Do not overbeat, or the frosting will be too runny.
Add about one-third of the powdered sugar and beat on low speed until just combined.
Scrape the sides of the bowl and beaters from time to time.
Add the remaining sugar gradually, beating until the frosting is smooth and creamy.
If too runny, add a little more sugar; if too thick, add a little more sour cream.
Incorporate the shredded coconut into the frosting.

Assembly: Cut the cakes in half horizontally.
Place each half on a plate, hollow side up.
Cover with half of the coconut frosting, taking care to leave a border around the edges.
Top with the other half of the cake.
Spread the remaining coconut frosting on top.
Decorate with toasted shredded coconut flakes.
It’s best to refrigerate the cake for several hours or overnight before serving.