Melt 2 tablespoons butter in a medium saucepan over medium heat. Add shallot, chopped carrots, bay leaf, and 1 teaspoon salt. Cover, and cook, stirring occasionally, until carrots are tender, 20 to 25 minutes. (Reduce heat to medium-low after 15 minutes if needed to prevent carrots or butter from browning.)
Stir in cream. Bring mixture just to a simmer, and immediately remove from heat; discard bay leaf. Using a blender or a food processor, puree mixture (use caution when puréeing hot liquids in a food processor). Transfer carrot purée to a small bowl; set aside.
Melt 4 tablespoons butter in a medium saucepan over medium heat. Stir in flour with a wooden spoon; cook, stirring constantly, 3 minutes. Whisk in milk gradually. Use a rubber spatula to scrape bottom and corners of pan.
Reduce heat to low. Cook, stirring often to prevent lumps from forming, 15 minutes. Whisk in carrot purée, and remove from heat. Stir in nutmeg, ginger, and 1 teaspoon salt; season with pepper. Transfer to a large bowl; let cool completely, about 30 minutes.
Preheat oven to 200 degrees C. Lightly butter eight 170g ramekins; set aside.
Add yolks, one at a time, to carrot mixture, whisking well after each addition.
Using a clean whisk or an electric mixer, beat egg whites until soft peaks form. Fold into carrot mixture.
Ladle mixture into prepared ramekins, filling almost to the rims. Place ramekins in a roasting pan, and transfer to oven. Pour enough boiling water into pan to come about three-quarters of the way up sides of ramekins. Bake until soufflés are puffed and set, and tops begin to brown, about 35 minutes. Using tongs, carefully transfer the soufflés to a wire rack, and let cool 10 minutes.
Before serving, bring a medium pot of water to a boil; add 2 teaspoons salt. Add spring carrots; cook 2 minutes. Add peas; cook until carrots are tender and peas are bright green, about 2 minutes more.
Melt remaining 2 tablespoons butter in a small saucepan over low heat. Drain vegetables; toss with the melted butter.
Invert each soufflé onto a metal spatula, and then invert again onto a serving plate. Arrange carrots and peas on each plate. Garnish with pea shoots.
You can make the soufflés a day ahead and refrigerate them, covered, in the ramekins. To reheat, unmould the soufflés and place them right side up on a rimmed baking sheet. Pour one-quarter cup heavy cream over top, and heat in a 190-degree oven until heated through and cream is bubbling, about twelve minutes. Prepare the vegetables while the soufflés are in the oven.