Preheat oven to 175°C (350°F). Grease and line a 9x13-inch (23x33 cm) sheet pan.
In a bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat butter and granulated sugar until creamy and fluffy.
Add eggs one at a time, beating well after each addition. Stir in 2 teaspoons vanilla extract.
Alternate adding the dry ingredients and whole milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour batter into the prepared pan and smooth the surface.
Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean.
While the cake bakes, prepare the caramel topping: In a saucepan over medium heat, combine brown sugar, heavy cream, and butter. Stir continuously until the mixture boils and thickens slightly, about 5 minutes. Remove from heat and stir in 1 teaspoon vanilla extract.
Once the cake is out of the oven, immediately pour the warm caramel sauce evenly over the cake.
Sprinkle toasted shredded coconut on top, pressing lightly so it adheres to the caramel.