While the poaching liquid will be prepared next, make the sauce first so it's ready when the salmon finishes cooking. In a small bowl, whisk together the Greek yogurt, Dijon mustard, fresh dill, minced garlic, lemon juice, extra-virgin olive oil, and ground pepper until smooth and well combined. Taste and adjust seasoning with a pinch of salt if needed. Set aside at room temperature. I find whisking the sauce a few minutes ahead allows the flavors to meld beautifully, making it taste more cohesive by the time you serve it.

Pour the water and dry white wine into a large skillet or shallow pan that's wide enough to accommodate the salmon fillets comfortably. Add the smashed garlic cloves, fresh dill sprigs, and 1/2 teaspoon kosher salt. Arrange the lemon slices in the liquid as well—they'll add brightness to the poaching liquid and prevent the salmon from sticking to the pan bottom. Bring this mixture to a gentle simmer over medium-high heat, which should take about 2-3 minutes.

While the liquid reaches a simmer, pat the salmon fillets dry with a paper towel and season the flesh side evenly with 1/8 teaspoon kosher salt. Gently place the salmon skin-side down into the simmering poaching liquid, nestling it among the lemon slices. The liquid should come about halfway up the sides of the salmon; if it doesn't, add a splash more water or wine. I prefer keeping the skin-side down because it protects the delicate flesh and keeps it moist during cooking.

Reduce the heat to medium-low and cover the pan with a lid or foil. Poach the salmon for 5 to 10 minutes, depending on the thickness of your fillets—thinner fillets closer to 1/2 inch will take 5 minutes, while thicker 1-inch fillets need closer to 10 minutes. The salmon is done when it flakes easily with a fork and the thickest part reaches an opaque, pale pink color. The gentle heat ensures the salmon cooks evenly and stays incredibly moist.

Carefully transfer the cooked salmon fillets to serving plates using a slotted spatula, letting any excess poaching liquid drip back into the pan. You can leave the skin on for presentation or gently slip it off—both are delicious. Discard the poaching liquid and aromatics (or reserve for making stock if desired). Place a generous spoonful of the dill sauce from Step 1 alongside or on top of each salmon fillet, and add any remaining lemon slices from the poaching liquid as a fresh garnish.