Boil the eggs for about 6-7 minutes (depending on size) and peel them once they have cooled.
Put the butter in a pot and let it melt.
Add the flour and mix it into the melted butter.
Then gradually pour in the milk while whisking continuously. Continue until the sauce reaches a consistency you are satisfied with. This takes 5-10 minutes.
Finally, add the mustard and, if needed, season with salt. Personally, I use fish mustard, so I don’t add salt.