Bring milk, butter, and salt to a simmer in large sauce pan over medium-high heat.
Add flour all at once, reduce heat to medium-low, and beat rapidly with a wooden spoon. Continue beating until a dry film forms on the bottom of the pan. Remove from heat.
After three minutes, add the pepper, basil, and nutmeg. Stir to incorporate.
Add eggs one at a time, beating each in thoroughly before adding the next.
Transfer to Ziplock freezer bag, squeeze out air, seal, and refrigerate 1 hour.