Prepare this cornbread at the last minute so you can serve it piping hot.
Combine cornmeal and next 3 ingredients in a bowl; stir in half-and-half and 1 tablespoon oil. Gradually add boiling water, stirring until batter is the consistency of grits. Stir in 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 well on paper towels. Serve immediately with softened butter.
Note: Stone ground (coarsely ground) cornmeal requires more liquid.