Since this sauce requires constant stirring, I recommend measuring and prepping all ingredients and having them close by so that you can add them in the order given.
Heat olive oil in a small saucepan over medium heat, then add diced shallot and cook for 3 minutes until softened. Add minced garlic during the last 30 seconds, taking care not to burn.
Deglaze with white wine, then add butter and stir until melted. Simmer over medium heat for 5 minutes, or until sauce reduces by half, stirring constantly.
Reduce heat to low and stir in heavy cream, mustard, lemon juice, and zest. Simmer gently, while whisking, for 5 minutes or until the sauce begins to thicken. Add chopped dill, salt, and pepper, then cook for another 5 minutes or until thickened.
Notes
To prevent your sauce from separating, do not let it boil. Try to keep it at a gentle simmer over very low-medium heat, while constantly stirring or whisking.
This lemon dill sauce is best when enjoyed immediately after cooking, but you can store leftovers in an airtight container in the refrigerator.
Refrigerated sauce will solidify and can be used as a spread on toasted bread or sandwiches.
If you wish to reheat this lemon dill sauce, I recommend using a double-boiler as you would with a hollandaise sauce, or microwaving it in 10-second intervals, stirring vigorously in between until the sauce is revived.
When reheating lemon dill sauce, you should aim to make it lukewarm, not hot. The more you heat it, the more you risk it separating.