Awaken the Nuts : Place the pistachios in a small, dry skillet over medium heat. Toast for 3–4 minutes, shaking the pan frequently, until fragrant and lightly golden. Immediately transfer to a small plate to cool completely.
Prepare the Ensemble : Pat the chicken cutlets dry with a paper towel and season all over with approximately 0.9 g of the sea salt and 0.3 g of the white pepper. Set aside. Prepare the strawberries and mint and have them ready for assembly.
Blend the Jewel-Tone Glaze : In a blender, combine ¾ cup (approximately 112 g) of the sliced strawberries, the tomato paste, and a small pinch of the remaining salt and pepper. Blend on high until completely smooth. Pour the glaze into a small bowl and set aside. Do not rinse the blender.
Whisk the Vinaigrette : To the same blender pitcher, add the remaining ¾ cup (approximately 112 g) of sliced strawberries, the white balsamic vinegar, the remaining approximately 1 g of sea salt, and the remaining approximately 0.4 g of white pepper. Blend until liquefied. With the blender running on low, slowly drizzle in the olive oil until the mixture is smooth and emulsified.
Pan-Sear the Cutlets : Set your cast-iron grill pan over medium-high heat until it is very hot, around 205°C (400°F). Lightly oil the pan. Place the seasoned chicken cutlets on the hot surface and cook for 3–4 minutes per side, until golden-brown and cooked through. In the final minute of cooking, generously brush the tops of the cutlets with the jewel-tone glaze. Flip and sear for 30 seconds more. The chicken is done when an instant-read thermometer registers 74°C (165°F) at the thickest point.
Rest and Assemble : Transfer the glazed chicken to a cutting board and allow it to rest for 5 minutes before slicing it into strips. While the chicken rests, combine the baby spinach, toasted pistachios, crumbled goat cheese, torn mint, and the remaining sliced strawberries in a large bowl.
Compose the Salad : Drizzle about half of the vinaigrette over the salad ingredients and toss gently to coat everything lightly. Divide the salad among three plates. Top each salad with a sliced chicken cutlet and serve immediately, passing the extra vinaigrette at the table.