Heat a skillet over medium heat and add the olive oil. Add the minced shallots and sauté until softened, about 2–3 minutes.
Add the minced garlic to the shallots and sauté until fragrant, about 30–45 seconds. Remove the pan from the heat and set aside.
In a medium saucepan, combine the balsamic vinegar, brown sugar, Dijon mustard, and sliced strawberries. Stir in the cooked shallots and garlic.
Bring the mixture to a boil over medium-high heat, then reduce heat and simmer, stirring occasionally, until the sauce thickens and coats the back of a spoon, about 12–15 minutes.
Preheat the oven to 425°F (220°C). Line a baking sheet with foil or a nonstick liner and place the salmon fillets skin-side down, spaced a couple inches apart. Season generously with kosher salt and freshly ground black pepper.
Roast the salmon in the preheated oven until nearly cooked through, about 10 minutes per inch of thickness (approximately 8–12 minutes depending on fillet thickness).
Remove the salmon from the oven and brush some of the strawberry glaze over each fillet.
Turn the oven broiler on high and broil the glazed salmon 1–2 minutes, watching closely, until the glaze bubbles and lightly browns.
Remove from the oven and serve the salmon with the remaining strawberry sauce spooned over the fillets.