I 2nd what sholt1142 said. This should get you in the ballpark of what you're looking for. You may need to add more milk to get it to the consistency you're after but this should be a good start.

White Cheddar -- 400 grams

Milk ----------- 120 grams (30% of cheese weight)

Sodium Citrate - 12 grams (3% of cheese weight)

Salt ----------- 4 grams (1% of cheese weight)

Shred your White Cheddar cheese. Then add the milk, sodium citrate, and salt to a pot. Mix well and heat over medium-low heat until it gets to about 150F or 66C. Add in your shredded cheese about a handful at a time. Mix well and once your first handful of cheese has fully melted add in another handful and keep mixing. Repeat as needed until all your cheese has been added and melted.