1. Combine first 2 ingredients and 1 1/2 cups water in a large bowl; whisk in honey until salt is dissolved and honey is blended. Add strawberries; cover and let stand 1 hour.
2. Pour strawberry mixture through a wire-mesh strainer into a medium bowl; reserve 2 Tbsp. liquid. Transfer strawberries to a bowl. Season with kosher salt and freshly ground pepper to taste.
3. Whisk together 1 Tbsp. vinegar, Dijon mustard, and reserved 2 Tbsp. strawberry liquid in a bowl. Add oil in a slow, steady stream, whisking constantly until smooth.
4. Cut lettuce hearts in half crosswise, keeping top 6 inches of each and reserving ends for another use. Place lettuce tops on a serving platter. Top with strawberries, pecans, and, if desired, cheese; drizzle with vinegar mixture.
*1 (4-oz.) goat cheese log, crumbled, may be substituted.