Heat the oil or butter in a medium saucepan over medium heat until shimmering, and add the sliced jalapeños. Cook for 2-3 minutes until they start to soften and release aroma.
Add the diced tomatoes and cumin to the jalapeños, stirring well. Cook for another 2 minutes, allowing the flavors to meld and the mixture to become more fragrant.
Reduce the heat to low and pour in the shredded cheese, stirring constantly to melt uniformly and create a smooth, cheesy sauce.
Gradually add the milk, stirring to loosen the cheese mixture to a dip-like consistency. Continue to stir until the mixture is thick but smooth and bubbling slightly around the edges.
Once the dip is ready, remove from heat and give it a final stir to ensure all ingredients are well combined and heated through.
Serve the cheesy jalapeño dip hot, scooped into a bowl or directly from the pan for dipping with chips, bread, or vegetables.
