In a medium bowl, toss the shrimp with 2 teaspoons of the soy sauce and 2 teaspoons of the sherry. Set aside.
Cut the green parts of the green onions into 1/4-inch lengths and reserve in a bowl large enough to hold the shrimp. Mince the white parts of the green onions and in a small bowl, combine them with the garlic, ginger and 2 teaspoons of the oil. Set aside.
In a medium bowl, combine the chicken broth, lemon juice, the remaining 1/4 cup sherry, the remaining 2 tablespoons soy sauce, the cornstarch and pepper and mix well. Set the sauce aside.
In a large nonstick skillet (or wok) over high heat, add 1 teaspoon oil and heat just until it is smoking. Add the shrimp and cook, stirring occasionally, until they are curled and bright pink, about 1 1/2 minutes. Transfer to the bowl with the scallion greens.
Add 1 teaspoon oil to the skillet and return to high heat until the oil is shimmering. Add the asparagus and cook, stirring occasionally, until it is crisp-tender, 2 to 3 minutes. Remove from pan. Add the remaining 1 teaspoon oil and the carrots to the skillet and cook, stirring occasionally, until they are crisp-tender, about 2 minutes. Return the asparagus to the skillet. Make a well in the center of the skillet and add the garlic-ginger mixture. Cook, mashing the garlic-ginger mixture until it is fragrant, about 30 seconds. Incorporate the mixture into the vegetables. Add the green onion tops and the shrimp and stir to combine.
Whisk the sauce to recombine, then add it to the skillet and heat until bubbles just break the surface. Remove from the heat and toss to coat all ingredients with the sauce. Add salt and pepper to taste and serve promptly with jasmine rice.