In a 8- or 10-inch cast-iron or nonstick skillet, heat 1 teaspoon oil over medium-high until shimmering. Add cubed ham steak and cook, stirring frequently, until ham is lightly browned, about 4 minutes; set aside.

In a large bowl or centered in a round bundt cake pan, stand each corn cob upright and slice off kernels into bowl with a sharp knife; reserve cobs. Don’t worry about getting every last millimeter of kernel; only trim as close to the cob as your knife can comfortably slice without encountering much resistance. When all 6 six cobs are trimmed, you should have about 4 cups (20 ounces) of kernels. (See The Best Way to Cut Corn Kernels From the Cob .) Alternatively, place 1 cob flat on cutting board. Hold the cob firmly in place with one hand, and with a sharp knife, slice off kernels, rotating the cob as needed (about 4 to 5 rotations will be needed).

Working with one cob at a time, scrape the back of your knife back and forth across the cob to extract the corn “milk” into a fine mesh strainer set over a large sauté pan or saucepan. You should have quite a bit of crushed kernel in addition to the juice. Using a spatula, press the mixture firmly into the strainer to extract as much liquid as possible. Remove strainer and discard fibrous corn solids.

Add cooked ham, cut corn kernels, whole milk, cream cheese, garlic, salt, and cayenne to the saucepan with the corn “milk.” Cook over medium-high heat, stirring frequently, until cream cheese is fully melted and the sauce is smooth, about 10 minutes. While cooking, adjust heat as necessary so that sauce is just bubbling around the edges; do not let it come to a boil. Add both shredded cheeses and continue to cook until the cheese is melted through and the mixture is glossy and as thick as nacho cheese, about 1 minute. Serve immediately, sprinkling individual portions or serving bowl with sliced scallions.