Preheat an outdoor grill for medium heat and lightly oil the grate.
Combine olive oil, balsamic vinegar, garlic, mustard, salt, and pepper in a small container with a lid. Cover and shake vigorously to combine dressing ingredients. Set aside.
Brush peach slices lightly with avocado oil. Place peaches, cut-side down, onto the grill; cook until grill marks form, 1 to 2 minutes. Turn each slice and cook until grill marks form, 1 to 2 minutes more. Remove from grill
Divide spinach between 4 salad plates. Top each salad with 4 grilled peach slices. Evenly distribute raspberries and top with some almonds. Drizzle each salad evenly with dressing.