
Wash and dry the dill and chives and then finely chop the herbs. Set aside.
Melt the butter in the microwave in a microwave-safe bowl. Place the melted butter in a bowl that's large enough to whisk the sauce in.
To the butter, add the olive oil, honey, mustard (both dijon and whole grain), and vinegar.
Vigorously whisk the mixture until you have a creamy emulsified sauce.
Taste and add salt to your preference if needed. You can also add honey or vinegar to balance the flavor to your taste.
Once the mustard sauce is seasoned and adjusted to your liking, add the chopped herbs and whisk to combine.
Pour the sauce into a bowl and serve alongside gravlax or other seafood dishes or meat dishes or roasted veggies etc.