Heat the oil in a large skillet set over medium-high heat.
Pat dry the salmon fillets with paper towels, then season them with salt and pepper and transfer them to the skillet, skin-side down.
Cook for about 5 to 8 minutes or until browned and cooked about three-quarters of the way through. The cooking time will depend on the thickness of the salmon.
Flip over and cook for 2 to 3 more minutes or until cooked through; remove from skillet and set aside. Add more oil as needed.
Add butter to skillet and melt over medium heat. Stir in the garlic and cook for 20 seconds, stirring very frequently.
Stir in the cherry tomatoes and season with salt and pepper. Continue to cook for 1 to 2 minutes or until tomatoes begin to soften.
Add in the spinach and cook for 1 minute or until the spinach is beginning to wilt.
Whisk in the evaporated milk, parmesan cheese, basil, and parsley; bring to a simmer. Reduce heat to low and cook for 2 minutes.
Add the salmon fillets back to the skillet and continue to cook for 3 minutes or until the salmon is heated through.
Remove from heat.
Spoon sauce over each fillet and serve.