1. Make the pickled scallions: In a medium saucepan set over medium-high heat, bring the Champagne and cider vinegars, ½ cup water, sugar, jalapeño, bay leaf and coriander seeds to a boil. In a 9-inch-square baking dish, add the scallion bottoms. Pour the pickling liquid over the scallions; make sure the scallions are submerged. Cool to room temperature, then cover with plastic wrap and refrigerate overnight or up to 2 weeks.

2. Make the scallion butter: Fill a medium bowl with ice and water and set aside. Bring a medium saucepan filled with water to a boil. Add the scallion tops and once they wilt, after about 1 minute, use tongs to transfer them to the ice water to stop their cooking. Place them on a paper-towel-lined plate to drain.

3. Heat a grill pan over high heat until smoking, about 2 minutes. Add the chives and char on both sides, about 2 minutes total. Add the charred chives to a food processor. Squeeze out the excess water from the cooked scallion tops and add them to the food processor along with 3 finely chopped pickled scallions, the butter, salt and pepper. Process until smooth, then transfer to an airtight container and refrigerate until the butter is chilled.

4. In a large pot of boiling, salted water, cook the pasta about 2 minutes shy of the package instructions for al dente. Add the radishes and, after 1½ minutes, the peas. Finish cooking the pasta until al dente, the radishes until crisp-tender and the peas until warmed through, about 1 minute more.

5. Drain the pasta and vegetables in a colander and place in a large serving bowl. Add about half of the scallion butter (reserve the remaining butter for another time) and stir until melted. Top with lots of grated Pecorino, toss and serve immediately.