For salad dressing, combine 2 tablespoons olive oil, white wine vinegar, lemon juice, parsley, garlic, Italian seasoning, and Dijon mustard in a small bowl. Stir rapidly with a fork or whisk, until well blended.
Stir in mayonnaise. Taste; season with salt and pepper. Stir in sugar, to taste. Refrigerate dressing until the salad is ready to be tossed.
Heat 2 tablespoons olive oil in a large, nonstick skillet over medium-high heat. When oil is hot, add asparagus pieces and cook, stirring frequently, for 3 to 4 minutes. Asparagus should be bright green and still crunchy. Remove from the skillet and set aside.
Melt butter in the same skillet; turn heat down to medium-low. Add orzo and stir to coat completely in the melted butter. Cook and stir continuously until orzo is a light, golden brown, about 4 minutes.
Add broth, stir, and bring to a boil. Cover, reduce heat to a simmer, and cook about 15 minutes. Remove the cover for the last five minutes, to assure that the water cooks away. Stir occasionally, to allow evaporation.
Remove orzo from the skillet and place in a bowl; drizzle with remaining 2 tablespoons olive oil, stir to coat the pasta, and refrigerate for about 15 minutes.
Meanwhile, for salad, combine asparagus, olives, cherry tomatoes, carrots, feta cheese, and red onion in a bowl.
Stir in cooled orzo and salad dressing, and toss to combine. Garnish with fresh parsley and serve cold.
