Pat the salmon fillets dry with paper towels and season both sides with salt and freshly ground black pepper.
Heat a large nonstick skillet over medium-high heat; if needed, use two skillets or cook in batches so the fillets are not overcrowded.
Add about 1 1/2 tsp olive oil to each skillet. Place the salmon in the hot skillet, presentation side down, and sear until the bottom is golden, about 4 minutes.
Flip the fillets and cook until desired doneness, about 2–3 minutes more. Transfer the salmon to a plate, tent with foil, and leave the pan oil in the skillet.
In a small liquid measuring cup or bowl, whisk the cornstarch with 1 Tbsp of the heavy cream until smooth, then add enough additional cream to total 1/2 cup. Stir in the Dijon mustard and honey; set aside.
Return the skillet with the reserved oil to medium heat and add the minced garlic; sauté until just barely golden, about 20–30 seconds.
Pour in the chicken broth and bring to a simmer, then reduce the heat to medium-low and simmer until reduced by about two-thirds, about 3 minutes.
Whisk the cream mixture once more and pour it into the skillet. Cook, stirring, until the sauce comes to a gentle simmer and thickens slightly, about 30 seconds.
Remove the pan from the heat, stir in the minced fresh dill, return the salmon to the skillet, and spoon the sauce over the fillets. Serve warm.