A Southern Breakfast

INGREDIENTS

• 1 cup all-purpose flour
• 1 cup cake flour
• 2 tsp. baking powder
• 1/2 tsp. baking soda
• 1/2 tsp. kosher salt
• 6 Tbs. chilled unsalted butter, plus more for serving
• 3/4 cup buttermilk
• 2 cups water
• 1 1/2 cups whole milk
• 3/4 cup old-fashioned white hominy grits, preferably stone-ground
• 5 Tbs. unsalted butter
• 1 clove garlic, minced
• 1 smoked ham steak, about 1 1⁄4 lb.
• 3/4 cup brewed coffee
• 1 tsp. sugar
• 8 large eggs
• 1/3 cup heavy cream or whole milk
• 1/8 tsp. freshly ground pepper
• 1/2 cup shredded sharp cheddar cheese