Bring a wide pot of salted water to a boil. Trim the baby carrots, leaving just 1/2 inch of the green tops, then peel and halve lengthwise. Trim the spring onions, removing the root and all but 2 inches of the tops, and halve lengthwise. Snap or cut off the tough ends of the asparagus and peel the bottom half of each. Cut each spear in half crosswise (or into thirds, if long).
Fill a large bowl with ice water. Add the carrots to the boiling water; cook until crisp-tender, about 6 minutes. Transfer with a slotted spoon to the ice bath to cool, then remove to a colander to drain. Add the spring onions to the boiling water; cook until crisp-tender, about 3 minutes, then cool in the ice water and remove to the colander. Repeat with the asparagus, cooking about 3 minutes. Pat the vegetables dry with a clean towel. (The vegetables can be prepared up to this point several hours ahead; cover and refrigerate.)
Heat the olive oil in a large skillet over medium-high heat until shimmering. Add the spring onions; sprinkle with the sugar, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring once or twice, until golden brown, about 3 minutes. Reduce the heat to medium; push the onions to one side of the skillet. Add the vinegar, mustard and 1/4 cup water to the other side of the skillet, whisking to combine; bring to a simmer and cook until thickened, 2 minutes. Toss with the onions. Remove from the heat and let cool slightly.
Add the carrots, asparagus, parsley and dill to the skillet; toss to combine.