Blanch the string beans in a large pot of boiling salted water for 1 minute only. Lift beans from water with a slotted spoon or sieve and immerse them in a bowl of ice water. Add the snap peas to the same boiling water and cook for 1 minute, until al dente, adding them to the ice water and beans. Cut asparagus in 2-inch lengths diagonally and cook in the boiling water for 2 minutes, and add to ice water. Cut broccolini in half, boil for 1 minute, and add to the ice water. When all the vegetables in the water are cold, drain well.
When ready to serve, heat the butter and oil in a very large saute pan or large pot. Saute the shallots over medium heat for 5 minutes, tossing occasionally, until lightly browned. Add drained vegetables to shallots with 1/2 teaspoon salt and the pepper; toss. Cook just until the vegetables are heated through. Serve hot. Makes 4 to 6 servings.