Preheat oven to 400°F. Toss squash with 2 teaspoons oil; sprinkle with salt and pepper. Toss mushrooms with 1 teaspoon oil; sprinkle with salt and pepper. Spread on separate baking pans and roast until tender, about 25 minutes for squash and 20 for mushrooms.
While vegetables are cooking, in a heavy-bottomed saucepan, heat 1 tablespoon oil over medium heat. Add orzo and cook for 5 minutes, stirring frequently, until it starts to brown. Add 2 cups water and 1/2 teaspoon salt and bring to a boil, stirring frequently. Reduce heat to low, cover and simmer for 20 minutes or until all the water is absorbed.
Transfer orzo to a mixing bowl and add 3 tablespoons oil and the vinegar and rosemary and mix well. Add green onions, squash and mushrooms; season with salt and pepper and fold in Kerrygold Aged Cheddar. Serve warm or room temperature.