Fresh mint appears twice here: finely chopped mint in the dressing and whole mint leaves in the strawberry chicken salad, tossed with tender greens.
Preheat grill to medium-high. (No grill? See Tip.) Brush chicken with 1 Tbsp. oil and sprinkle with 1/4 tsp. each salt and pepper. Grill, turning once, until cooked through, 2 to 3 minutes per side. When cool enough to handle, slice the chicken.
Meanwhile, whisk vinegar, shallot, honey, and the remaining 5 Tbsp. oil, 1/2 tsp. salt, and 1/4 tsp. pepper in a large bowl. Finely chop 1/4 cup mint; add to the dressing in the bowl, whisking to combine. Reserve 2 Tbsp. of the dressing.
Tear or coarsely chop the remaining 3/4 cup mint leaves; add to the bowl along with mixed greens. Toss gently to combine. Divide the salad among 4 dinner bowls. Combine the chicken and the reserved 2 Tbsp. dressing in the large bowl; stir to coat. Divide the chicken, strawberries, snap peas, goat cheese, and almonds among the 4 dinner bowls. Garnish with more mint, if desired.
Tip: No grill? Preheat broiler to high. Prepare chicken as directed in Step 1 and broil on a large baking sheet 3 to 4 inches from the heat source, flipping once, until it reaches an internal temperature of 165 degrees F, 4 to 6 minutes per side.