Combine 1 tablespoon oil, vinegar, honey, thyme, 1/4 teaspoon pepper, and 1/8 teaspoon salt in a medium bowl; stir with a whisk. Add 1 cup strawberries, tossing to coat. Let stand at room temperature 10 minutes.
Heat a medium skillet over medium-high heat. Brush chicken with remaining 1 teaspoon oil; sprinkle evenly with remaining 1/8 teaspoon pepper, salt, and paprika. Coat pan with cooking spray. Add chicken to pan; cook 2 to 3 minutes on each side or until done. Remove chicken from pan; let stand 5 minutes. Cut across the grain into slices.
Divide spinach, remaining 1 cup strawberries, and onion between 2 plates. Top evenly with chicken slices and strawberry-balsamic mixture. Top each serving with 1 1/2 tablespoons pecans and 2 tablespoons cheese.