Melt butter in a saucepan and whisk in the flour to form a roux.
Stir in garlic paste, green chillies, tomatoes, and milk, and continue stirring over low heat until sauce thickens.
Remove pan from heat and gradually add cheeses, stirring constantly, allowing them to melt into the sauce. If the cheese doesn’t continue to melt, put back on the heat just to warm it enough to melt the cheese, but be careful not to boil, otherwise the sauce becomes grainy and stringy, and can seize up. Very low heat is the key here, using as little heat as you can.