Tear or cube your white American cheese into smaller pieces to help it melt evenly. Open and drain your green chiles. Measure out your salsa and milk, so you have everything ready before you start cooking.
Place a heavy-bottomed saucepan over low to medium-low heat. Avoid using high heat, as it can make the cheese grainy. Cooking on low heat will give you a smooth and glossy finish.
Add the cheese pieces in small handfuls, stirring constantly with a silicone spatula. Wait for each handful to melt before adding the next. This process takes about 4 to 5 minutes, so be patient.
Once the cheese is melted and smooth, stir in the salsa and drained green chiles. Mix well until everything is combined. The queso will thicken a bit, which is normal.
Pour in the milk a little at a time, stirring after each addition until it reaches a smooth, pourable consistency. It should be thin enough to coat a chip but not watery. Start with ¼ cup and add more if needed.
Stir in the cumin and garlic powder. Taste the queso and add salt only if needed. Usually, the salsa and cheese are flavorful enough on their own. Pour the queso into a warm bowl or transfer it to a small slow cooker set to warm. Serve right away with tortilla chips.