Place a large roasting pan or jelly-roll pan in oven and Preheat oven to 500°.
Combine Broccolini, 1 tablespoon oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a bowl; toss to coat.
Combine mushrooms, 1 tablespoon oil, and 1/8 teaspoon salt in another bowl; toss to coat.
Combine shrimp, remaining 1 tablespoon oil, 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper in another bowl; toss to coat.
Arrange Broccolini and mushrooms side by side on one half of hot roasting pan (leave other half of pan open for shrimp). Roast at 500° for 8 minutes. Add shrimp to pan. Roast vegetables and shrimp 4 minutes or until shrimp are done.
Place remaining 1/8 teaspoon salt, butter, and 2 tablespoons water in a small saucepan over medium-high heat; bring to a simmer. Remove pan from heat; stir in chives. Serve sauce with shrimp and vegetables.