Warm the oil in a large nonstick skillet over medium-high heat. Season salmon all over with salt and pepper. When oil is shimmering but not smoking, add salmon skin side UP and cook until the flesh is deeply golden, about 5 minutes. Flip over and cook 2 minutes more. Transfer to a plate.
Reduce heat to medium and add butter. When butter has melted, stir in garlic and cook until fragrant, about 20 seconds. Add cherry tomatoes and season with salt and pepper. Cook until tomatoes are beginning to burst, then add spinach and cook until just wilted.
Stir in heavy cream, Parmesan, and parsley (and/or basil) and bring mixture to a simmer. Adjust heat so it's just a gentle bubble and cook until sauce is slightly reduced, about 3 minutes.
Return salmon back to skillet and spoon over sauce. Simmer until salmon is cooked through, about 2 to 3 minutes more.
Garnish with more herbs and squeeze lemon on top before serving.
