Combine condensed milk, evaporated milk, and heavy cream in a small jar or pitcher. When cake is cool, pierce the surface with a fork or toothpick several times. Slowly drizzle all but about 1/2 cup of the milk mixture—use a basting brush to get as much around the edges of the cake as you can. Save the remaining 1/2 cup for serving, if you want.
Allow the cake to absorb the milk mixture for at least 30 minutes.
To ice the cake, whip 1 3/4 cups heavy cream with 1 tsp of vanilla extract & 2 1/2 tablespoons of sugar until it's thick and spreadable.