Heat butter and olive oil in a skillet over medium heat
Add minced garlic and cook for 30–40 seconds until fragrant
Pour in broth and let it simmer for 2–3 minutes to reduce slightly
Lower heat and stir in heavy cream and Dijon mustard until smooth
Add salt, black pepper, lemon zest, and lemon juice
Simmer gently for 4–5 minutes until lightly thickened
Remove from heat and stir in dill and parsley
Spoon over cooked salmon and serve immediately
Notes
Keep heat gentle after adding cream to avoid separationFresh lemon juice and zest give the best flavorSauce thickens slightly as it coolsIf too thick, add a splash of warm broth or creamBest served fresh but can be refrigerated up to 1 day