In a medium saucepan, bring the milk to a boil over high heat. (Watch closely so it doesn't boil over).
Remove from heat and let sit for a minute. Stir in the 3 tbs of butter and the buttermilk. Stir until the butter has completely melted. Let mixture sit for about 2 minutes.
Pulse the corn kernels in a food processor until just coarse.
In a large bowl combine corn, cornmeal, sugar, salt, and Monterey Jack cheese. Stir to combine.
Gradually add enough of the hot milk mixture to make a very thick batter.
Heat griddle or large skillet over medium high heat, and melt 1-2 tbs of butter until the foam subsides.
Drop about 2 tbs of batter into the skillet for each arepa. (They should be about 3 inches in diameter) Cook until underside is golden brown, about 4 minutes, then flip and brown other side.
When the arepas are cooked on both sides and the batter is cooked through, sandwich 1 slice of mozzarella cheese between 2 arepas. Reduce heat to low, and continue cooking just until the cheese melts, turning once or twice. Continue filling and cooking the remaining arepas.