Bring a medium pot of salted water to a boil. Add broccoli florets and blanch for 45–60 seconds until bright green and slightly tender. Drain and immediately plunge into an ice bath to stop cooking. Drain and pat dry.

Heat a small skillet over medium heat. Add slivered almonds and toast, stirring frequently, until golden and fragrant, about 3–5 minutes. Remove from heat and cool.

Whisk together Greek yogurt, mayonnaise, honey, apple cider vinegar, and Dijon mustard in a small bowl. Season with salt and pepper. Thin with a teaspoon of water if needed.

In a large bowl, combine blanched broccoli, diced Honeycrisp apples, toasted almonds, raisins or cranberries, and red onion. Pour dressing over the salad and toss to coat. Garnish with chopped parsley. Chill for 15 minutes if desired before serving.