Heat large saucepan over medium heat. When pan is warm, add butter and let melt completely.
When butter is melted, sprinkle in all-purpose flour and whisk to combine. Cook mixture 1 minute, whisking frequently, until lightly browned.
Remove saucepan from heat. Slowly add 2 cups of half and half to saucepan, whisking constantly while adding, until mixture is smooth. Once smooth, pour in whole milk and remaining half and half. Whisk until mixture is fully combined and smooth.
Return saucepan to medium heat. Simmer, whisking frequently, until mixture has thickened to creamy soup-like consistency.
Remove saucepan from heat. Add salt, pepper, and paprika, and whisk to incorporate. Add 3 cups shredded cheese blend in increments, whisking until smooth between each increment. Repeat until all cheese has been added and completely melted, and mixture is completely smooth.
Add drained chile peppers and stir to incorporate.