Stir together chicken broth, milk, garlic, and onions into a small saucepan.
Cook on medium heat until the mixture is reduced to half. It should take 10-12 minutes.
Cut cold butter into 1-inch cubes. Add 1 cube of butter to a medium-size saucepan and heat on medium heat until it melts.
Add all-purpose flour and mix it well with the butter. Cook until the mixture turns slightly brown (1-2 minutes). Stir continuously while cooking.
Now slowly pour the reduced chicken broth mixture over the flour and butter mixture and whisk continuously using a wire whisk.
Cook for a minute until the sauce slightly thickens.
Add the remaining butter to the pan and cook until the butter slightly melts and combines with the sauce. Stir frequently.
Note – Make sure the butter is chilled. It will bring down the temperature of the sauce and the sauce will not curdle when lemon juice is added to it.
Add lemon juice before the butter completely melts and cook the sauce for 1-2 minutes.Note – Add the lemon juice when the sauce is not very hot. If you add lemon juice to the hot sauce, it might curdle it.
Season with salt and pepper to taste, and add parsley and mix well. The sauce is ready. Use it as desired.