Preheat oven to 350℉. Spray a 13-inch rectangle baking pan with nonstick cooking spray. Set aside.
In a large bowl, whisk together sugar, flour, cocoa powder, baking soda, baking powder and salt.
Add eggs, vanilla, yogurt, oil and warm water. Stir until well combined. Fold in ¾ cup of sweetened shredded coconut.
Pour batter into the prepared baking pan. Tap on the counter a few times to help the batter settle.
Bake in preheated 350℉ oven for about 30 minutes or until a toothpick inserted in the center comes out clean.
Using the tines of a fork poke holes into the top of the hot cake.
In a small bowl, whisk together the coconut cream and sweetened condensed milk until smooth. Slowly pour over the hot cake, using an offset spatula or the back of a metal spoon to spread evenly into the holes as you go. Cool completely and chill in the refrigerator for at least two hours or overnight.
Sprinkle 1 cup of coconut on a rimmed baking sheet and toast in the 350℉ oven for 5-7 minutes or until golden brown. Set aside to cool. Store in a ziploc bag if making ahead more than a couple of hours.
Frosting:
In a chilled metal bowl, beat heavy whipping cream until stiff peaks form; 1-2 minutes.
In another large bowl, beat softened cream cheese on high until fluffy; about 1 minute.
Add powdered sugar and vanilla extract and beat on high for 1-2 minutes.
Gently fold whipped cream into the cream cheese mixture. Chill frosting until ready to use, or spread immediately on chilled cake.
Frost the chilled cake with the whipped frosting. Sprinkle evenly with toasted coconut.
Store loosely covered in the refrigerator until ready to serve.
Notes
Frosting: Chill metal bowls and beaters or whisk attachment for at least 10 minutes in the refrigerator before using.
Storing: leftover cake in an airtight container in the refrigerator for up to 3-4 days.
Freezing: You can freeze the whole cake right in the pan if you want. Just cover tightly with plastic wrap, then tightly with foil and freeze for up to 3 months. Thaw in the fridge before slicing.
For freezing individual slices, I recommend flash freezing on a baking sheet, wrapping each piece in plastic wrap and foil, then placing into a freezer bag.