1- Gather all ingredients and ensure garlic is minced finely for even flavor distribution.

2- Heat olive oil in a skillet over medium heat and sauté garlic until fragrant but not browned, about 1-2 minutes.

3- Pour in heavy cream gradually while stirring, allowing the mixture to warm through and thicken slightly, approximately 3-4 minutes.

4- Stir in Dijon mustard thoroughly to combine with the creamy base, adjusting the quantity to taste.

5- Season the sauce with salt and freshly ground pepper, tasting and adjusting seasoning as needed.

6- Simmer the sauce gently on low heat for 5 minutes to fully blend the flavors while stirring occasionally.

7- For vegan or gluten-free variations, replace cream and mustard with substitutes at the start and follow the same method.

8- Finally, remove sauce from heat and drizzle over cooked salmon fillets, serving immediately for best flavor and texture.

9- Heat a large non-stick skillet over medium-high heat; use two skillets or cook in batches if needed to avoid overcrowding. Add 1 1/2 teaspoons olive oil to each skillet. Pat the salmon fillets dry with paper towels and season both sides with salt and pepper. Place the salmon in the skillet with the top side down. Let it sear undisturbed until the bottom is golden brown, about 4 minutes. Flip and cook for an additional 2 to 3 minutes to desired doneness.

10- While the salmon cooks, whisk together 1/2 teaspoon cornstarch with 1 tablespoon of the heavy cream in a liquid measuring cup. Add enough cream to reach a total of 1/2 cup, then whisk in 1 1/2 tablespoons Dijon mustard and 1/2 teaspoon honey. Remove the salmon from the skillet and transfer to a plate, leaving the oil in the skillet. Tent the salmon with foil to keep it warm. Add the 3 minced garlic cloves to the oil in the skillet and sauté over medium heat until just barely golden, about 20 to 30 seconds. Pour in 1/2 cup low-sodium chicken broth, bring to a simmer, and reduce the heat to medium-low. Let the broth reduce by about two-thirds, approximately 3 minutes. Whisk the cream mixture again, then pour it into the skillet. Cook and stir, bringing it to a simmer. Let it cook gently while stirring for about 30 seconds. Remove from heat, stir in 1 tablespoon fresh dill, return the salmon fillets to the pan, spoon the sauce over them, and serve warm.