In a food processor, combine the mustard, sugar, vinegar, and salt and pepper.
Turn the food processor on low and allow to continue mixing while you slowly pour the oil into the processor.
Once all the oil is in, continue running the food processor for one additional minute to filly emulsify the oil into the sauce. This will make the sauce thick and creamy.
Pour the sauce into a bowl and gently stir in the minced dill.
Enjoy.
Notes
This sauce can be stored in an air tight container in the fridge for up to 1 week.