Purée Sesame Crème, Allium Confit, chopped herbs, and vinegar in a blender on high speed, adding ice water by the tablespoonful as needed to achieve a pourable consistency, until smooth and creamy. Season sauce with salt and pepper.

Fill a large pot three quarters full with water, add reserved herb stems, and season heavily with salt. Bring water to a boil, then add carrots and cook until just tender, about 3 minutes. Using a slotted spoon, immediately transfer carrots to a large bowl of ice water and let cool.

Place potatoes in same pot and return to a boil. Cook until tender (flesh should be easy to pierce with a fork), about 10 minutes. Using slotted spoon, transfer potatoes to bowl of ice water and let cool. Drain carrots and potatoes; place in a clean large bowl and add half of the radicchio. Place mushrooms in a medium bowl.

Whisk Pumpkin Hot Sauce, oil, and chopped herbs in another medium bowl. Pour half of mixture over carrots and potatoes and the other half over mushrooms; toss each to coat. Season with salt and pepper.

Prepare a grill for medium-high heat. (Alternatively, heat a large cast-iron skillet over medium-high.) Grill mushrooms, turning occasionally, until deep golden brown and crisp around the edges (or cook in batches, stirring often, if using a skillet), 12–14 minutes. Transfer mushrooms to a large shallow serving bowl.

Grill carrots, potatoes, and radicchio, turning occasionally, until deep golden brown all over (or cook in batches, tossing often, if using a skillet), about 4 minutes. Transfer vegetables to bowl with mushrooms and toss to combine.

To serve, drizzle generously with sesame sauce; top with Spiced Pecans and remaining radicchio. Squeeze juice from each lemon half over.