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Preheat oven to 400 degrees.
Rub salmon all over with olive oil. Season generously with salt and pepper, then season with Italian seasoning.
Melt butter in a large skillet over medium-high heat. Brown salmon on each side for 1-2 minutes. Transfer to plate and cover to keep warm.
Add broth to pan. Stir in pesto and cream. Add salt and pepper to taste (I'm quite generous with the salt and pepper here!).
Return salmon to the skillet. Spoon some of the sauce over the salmon.
Transfer skillet to the oven and cook for 12-15 minutes until salmon is cooked through and sauce is thickened (enough to coat the back of a spoon).
Spoon sauce over salmon and serve immediately. Enjoy!