Combine first 4 ingredients in a bowl; stir in half and half and 1 tablespoon oil Gradually add boiling water, stirring until batter is consistency of grits. Stir in 1 to 2 cups finely chopped cooked country ham.
Pour oil to a depth of 1/2 inch into a large heavy skillet; place over medium-high heat. Scoop batter into a 1/4 cup measure; drop into hot oil, and fry, in batches, 3 minutes on each side or until golden. Drain on paper towels. Serve with softened butter.
NOTE: The amount of boiling water needed varies depending on the type of cornmeal used. Stone-ground (coarsely ground) cornmeal requires more liquid.