Whisk brown sugar and mustard powder in large bowl to combine. Add vinegar and honey; whisk well. Strain through a fine-mesh sieve into a large metal bowl. Add the eggs and whisk until blended.
Set bowl with a mustard mixture over a large pot of gently simmering water (do not allow bottom of bowl to touch water; you don’t want the eggs to scramble.) The bowl with the mustard mixture should be slightly smaller than the pot with the simmering water. This will help prevent the bottom from touching the water. Cook the mustard mixture, whisking and scraping the bottom of the bowl frequently, until mustard is thick and coats the back of a wooden spoon. If you have an instant-read thermometer the mustard is done when the thermometer registers 160 degrees. This should only take about 5 minutes.
Divide the mustard among the jars. Store in the refrigerator until ready to use. Mustard can be made 2 weeks ahead and will keep in the refrigerator for up to 2 months.
From Bon Appetit Magazine