Heat 2 Tbs. of the oil in a 12-inch skillet over medium heat until shimmering hot. Pat the chicken dry and season with 2 tsp. salt and 1 tsp. pepper. Cook, turning once, until just cooked through, about 10 minutes total. Transfer the chicken to a cutting board and let rest, loosely covered with foil, for 5 minutes.
While the chicken cooks, toast the almonds in a dry 10-inch skillet over medium heat, stirring occasionally, until evenly browned, 3 to 5 minutes. Transfer to a plate to cool.
In a small bowl, whisk the remaining 1/3 cup olive oil with the vinegar, honey, shallot, 1/2 tsp. salt, and 1/2 tsp. pepper. In a large bowl, combine the spinach, strawberries, blue cheese, and almonds and toss with enough of the dressing to coat. Arrange the salad on a platter or plates. Slice the chicken and arrange on the salad. Drizzle with some of the remaining vinaigrette, if desired, and serve.
Serve with a hunk of warm crusty bread and a glass of rosé.