Gradual.
Taste the two sauces and examine the way they look
when you put a spoonful on a plate. The sauce for
which the milk was added slowly should be far
smoother, with a glossy complexion, while the sauce
for which the milk was added rapidly will be much
thinner, with a grainy, broken appearance.
When adding liquid to a roux, the goal is to
disperse the flour as evenly as possible within the
liquid. By adding the liquid a bit at a time and
incorporating it gradually, you ensure that the
individual clumps of flour are broken up with the
whisk. If you add the milk too fast, the flour clumps
have plenty of space to flow around—many of them
end up avoiding the wires of the whisk, resulting in a
lumpier, thinner sauce.
So, what if you accidentally add your milk too