Pat the salmon fillets dry and season both sides with salt and pepper.
Heat 1 tablespoon of avocado oil in a large skillet over medium-high heat.
Place salmon in the pan skin side up and sear 4–5 minutes, then flip and cook 2–3 minutes more until cooked through (about 145°F internal temperature).
Remove the salmon to a plate and add the remaining 1 tablespoon of avocado oil to the skillet; reduce heat to medium.
Add the sliced shallot and minced garlic to the pan and sauté 1–2 minutes, stirring frequently, until fragrant and softened.
Pour in the vegetable broth and cook 1–2 minutes, scraping up any browned bits from the pan.
Add the milk and Neufchâtel to the skillet and whisk until the cheese melts and the sauce is smooth.
Bring the sauce to a gentle simmer and cook about 5 minutes until slightly thickened and able to coat the back of a spoon.
Stir in the juice of half a lemon, then add the salmon back to the pan to warm in the sauce.
Sprinkle the chopped dill and capers over the salmon and sauce, then serve immediately.