Stovetop method: Bring 1 inch of water to a boil in a medium saucepan. Reduce the heat to medium-low and place a bowl inside the pot to create a double boiler. (The bowl should be big enough to rest above the rim of the pot without the bottom touching the water.) Add both cheeses, the half-and-half, garlic, jalapeño, and ground black pepper, then stir to combine. Cook, stirring occasionally, for 5 to 10 minutes, until the cheese is melted and the dip is creamy. Stir in the green chilies.
Slow cooker method: Combine both cheeses, the half-and-half, garlic, jalapeño, and ground black pepper in the base of a slow cooker, and stir to combine. Cover and cook on high for 50 minutes, stirring once half-way through. Stir in the green chilies. Transfer to a serving bowl or reduce the temperature of the slow cooker to warm and keep covered until ready to serve.
Top with diced tomatoes, cilantro, and sliced jalapeño. Serve immediately.
Recipe Notes
Tip: If you are using sliced white American cheese from the deli, stack the slices about 1/2-inch high, then dice to create the perfect size for quick melting.