In a medium saucepan over medium heat, melt the butter. Add the flour and whisk constantly for about 1 minute until it forms a smooth paste and smells slightly nutty.

Slowly whisk in the milk and heavy cream, stirring to avoid lumps. Simmer until the mixture thickens slightly, about 2 to 3 minutes.

Add the cream cheese and stir until melted. Then add shredded cheddar and Monterey Jack cheese gradually, stirring until completely smooth.

Mix in diced green chilies, jalapeño (if using), garlic powder, onion powder, salt, and pepper. To combine all the flavors, boil it for a further two to three minutes.

Pour the queso into a serving bowl and serve immediately with tortilla chips or use it as a drizzle over burritos and nachos.