Pat pork dry with paper towels and sprinkle with 1 teaspoon kosher salt and ½ teaspoon pepper. In a 12-inch nonstick or well-seasoned cast iron skillet, heat 1 tablespoon oil over medium-high heat until just smoking. Add pork and cook, flipping every 2 minutes, until well browned and meat registers 135 to 140°F (57 to 50°C) on an instant-read thermometer, 8 to 12 minutes. Transfer to a carving board and let rest while preparing sauce and salad. Do not wipe out pan.
Add 1 tablespoon oil to remaining fond in skillet and heat over medium-high heat until shimmering. Add the finely chopped shallot, ¼ teaspoon salt, and ¼ teaspoon pepper and cook until softened, about 3 minutes. Add strawberries, vinegar, and sugar (if using), and cook, stirring frequently, until berries are softened and mixture is syrupy, about 5 minutes.
In a large bowl, whisk ½ cup of warm cooked strawberry mixture, remaining 2 tablespoons oil, and remaining ¼ teaspoon salt together. Add spinach, basil, pecans, and the sliced shallot and toss to combine. Top salad with crumbled goat cheese.
Slice the pork and serve it with salad. Serve remaining strawberry sauce on the side for the pork.
