Prepare the strawberry relish: hull and dice the strawberries and place them in a bowl.
Stir in the balsamic vinegar, 1/4 teaspoon heaping salt, 1/8 teaspoon black pepper, and the lemon zest; mix to combine.
Let the mixture macerate at room temperature for at least 30 minutes, stirring every 10 minutes, until juices form and flavors meld.
While the strawberries macerate, bring the salmon to room temperature (about 20–30 minutes) and preheat the oven to 425°F (218°C).
Pat the salmon fillets dry and season both sides generously with salt and pepper.
Heat a large ovenproof skillet over medium-high heat for 3–4 minutes until drops of water sizzle. Add 2 tablespoons olive oil and swirl to coat; oil may smoke lightly.
Carefully place the fillets in the hot skillet, skin-side up if using skin-on, without crowding the pan. Turn the burner to high.
Sear undisturbed for 2–3 minutes until a golden crust forms on the bottom edge where the fish contacts the pan.
Transfer the skillet to the preheated oven and roast for 6–10 minutes, depending on fillet thickness and desired doneness (about 7–8 minutes for 1-inch-thick fillets).
Remove the skillet from the oven with an oven mitt and transfer fillets to plates, crust-side up, using tongs or a fish spatula.
Chiffonade the basil: stack leaves, roll tightly lengthwise, then slice crosswise into thin ribbons; discard stems.
Stir the macerated strawberries, taste, and adjust seasoning if needed. Spoon about 1/2 cup of the berry relish over each fillet and sprinkle with equal amounts of chiffonaded basil; serve immediately.