To make the Texas caviar, stir together the black-eyed peas, tomatoes, jalapeños, red bell pepper, red onion, garlic, cilantro, salt, black pepper, cumin, olive oil, and lime juice until well combined. Taste and adjust seasonings. Refrigerate until ready to use. (This can be made a day ahead.)
Whisk together the cornstarch, half and half, and water until well combined, then pour into the pot. Turn the heat up a smudge to medium and while constantly stirring, bring to a simmer (don't let it come to a raging boil!) and cook until the mixture begins to thicken, which should happen in a couple of minutes.
For the American cheese, I prefer to get mine from the deli counter at the grocery store so you don't have to unwrap each individual slice. Kraft Deli Deluxe in the cheese aisle is a good option, too, as it also comes unwrapped.
Texas caviar chile con queso | www.homesicktexan.com