In a small bowl, whisk to combine the ramps, garlic, minced anchovies, lemon juice, and a big pinch each sea salt and pepper. Gradually whisk in the mayonnaise. Cover bowl and chill for an hour or longer.
Preheat oven to 450° F. Set a large rimmed baking sheet in the oven to preheat as well.
Set potato cubes in stock pot filled with cold water. Rinse and drain twice. Fill pot with water again and add juice from half a lemon.
With the remaining lemon half handy, peel the sunchokes, then rub each one all over with lemon. Slice into 3/4-inch cubes, tossing cut pieces with more lemon juice as you go, and place them in the stock pot with the potatoes as you finish.
Set stock pot over high heat and bring to a boil. Add 2 teaspoons sea salt. Once water comes to a boil, cook root vegetables for 1 minute. Drain. Toss with 2 tablespoons olive oil and 1/2 teaspoon each sea salt and pepper. Remove hot baking sheet from the oven and spread root vegetables over top. Roast for 15 minutes, carefully flip each sunchoke and potato, and then roast for another 15 to 20 minutes, or until vegetables are a deep golden brown.
Meanwhile, prep the asparagus. Rinse spears well and pat dry. Snap off woody ends (roughly the bottom third) and slice diagonally into 2 or 3-inch sections. Toss with the remaining 1 tablespoon olive oil, 1 teaspoon reserved lemon zest, sea salt, and pepper. Spread on a large rimmed baking sheet. Roast asparagus, shaking pan once halfway through, for 12 to 17 minutes, or until asparagus is tender and the edges have browned.
Cool vegetables for 10 minutes, then toss with several tablespoons dressing, minced herbs, and salt and pepper to taste. Serve right away.