Gather and prepare ingredients: Measure out all ingredients before you start. Mince 2 cloves garlic finely. Chop fresh dill (about 1 tablespoon). Chop capers (about 2 tablespoons). Zest 1 lemon using a microplane or zester. Juice 1 lemon to get about 2 tablespoons fresh juice. Have your measuring spoons and cups ready. Time: 5 minutes.

Melt butter and cook garlic: In a medium saucepan (8–10 inches wide), melt 3 tablespoons butter over medium heat. Heat should be medium — the butter will foam slightly but not brown. Once melted and foamy, add minced garlic immediately. Stir constantly with a wooden spoon or silicone spatula. Cook for 1–2 minutes until the garlic smells fragrant and slightly golden but not brown. Checkpoint: Your kitchen should smell of toasted garlic and the garlic should look pale golden, not dark.

Add broth and lemon juice: Pour in 1/2 cup chicken or vegetable broth slowly, then add 2 tablespoons fresh lemon juice. Stir well to combine. Bring the mixture to a simmer over medium heat. You'll see small bubbles breaking the surface. Let it simmer gently for 2–3 minutes to reduce slightly and concentrate flavors. The liquid should reduce by about 1/4 cup. Time: 3 minutes.

Add heavy cream: Reduce heat to medium-low — this step is important to prevent the cream from breaking. Slowly pour in 1 cup heavy cream while stirring constantly with your whisk or spoon. Stir in one direction continuously for about 1 minute. The sauce should start to look creamy and smooth, not separated. Checkpoint: The sauce should be smooth, homogeneous, and pale yellow. If you see any small lumps or separation, keep stirring gently.

Whisk in seasonings: Add 1 teaspoon Dijon mustard, 1/2 teaspoon honey, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/4 teaspoon white pepper. Whisk vigorously for 1–2 minutes until everything is fully blended and the color is even throughout. The sauce should smell bright and tangy. Taste a tiny spoonful (let it cool slightly) — it should be creamy, slightly sharp from the mustard, and balanced between savory and faintly sweet.

Add fresh herbs and capers: Stir in 1 tablespoon chopped fresh dill and 2 tablespoons chopped capers. Stir gently for 30 seconds to distribute the herbs and capers evenly throughout the sauce. The dill will add a fresh green fleck and herbaceous aroma. Checkpoint: You should see small flecks of green dill and dark capers throughout the creamy sauce.

Simmer and thicken: Keep the heat at medium-low and let the sauce simmer gently for 2–3 minutes. You should see a few small bubbles gently breaking the surface — not a rolling boil. Do NOT let it boil rapidly or the cream may separate. The sauce will thicken slightly as it simmers. Stir occasionally. After 3 minutes, the sauce should coat the back of a spoon lightly. Time: 3 minutes.

Final seasoning and lemon zest: Remove the saucepan from heat immediately. Stir in the lemon zest (about 1 teaspoon) from your microplane. This adds a bright citrus flavor and beautiful color flecks. Taste again — adjust salt or lemon juice if needed. The sauce should taste balanced: creamy, bright, herbaceous, and savory. Time: 1 minute.

Transfer and serve: Pour the sauce into a serving bowl or directly onto plates with cooked salmon fillets. The sauce should be pourable but thick enough to coat a spoon. Serve immediately while hot. If you need to hold it for up to 30 minutes, place a piece of plastic wrap directly on the surface to prevent a skin from forming, and keep it warm over very low heat or in a warm (not hot) spot. Time: 2 minutes.