Combine the flour and 1/2 teaspoon salt in a large bowl; make a well in the center. Add 1 cup ricotta and the egg to the well; gradually mix into the flour with a fork to form a shaggy dough. Turn out onto a lightly floured surface and knead into a smooth ball. Wrap in a kitchen towel and set aside for 30 minutes.
Meanwhile, blanch the vegetables: Prepare a bowl of salted ice water. Bring a medium saucepan of generously salted water to a boil. Add the scallions; boil until bright green, about 30 seconds. Transfer with a slotted spoon to the ice water. Boil the radishes, then the asparagus, cooking each until bright but still firm, 2 to 3 minutes, then plunging into the ice water. Drain the vegetables and set aside.
On a clean, dry surface, form the cavatelli (see instructions below).
Bring a large pot of salted water to a boil. Add the cavatelli; cook until they float and are tender, 3 to 4 minutes. Remove with a slotted spoon to a bowl (reserve the pasta water) and toss with 2 tablespoons butter, and salt and pepper to taste. Cover to keep warm.
Melt another 2 tablespoons butter with 3 to 4 tablespoons pasta water in a skillet over medium heat. Add the vegetables; toss until warm and glazed. Season with salt and pepper. Add the remaining 2 tablespoons butter and more pasta water to make a light sauce. Toss with the cavatelli; serve topped with dollops of the remaining 1/2 cup ricotta.
1. Divide the dough into 4 pieces. Work with one piece of dough at a time; cover the rest with a towel.
2. Roll the dough into a long 1/2 inch-thick rope, working from the center to the edges to maintain an even thickness as you go.
3. Cut the rope into 1/4-inch-wide pieces (we used a pastry scraper), pressing down and pushing away with each cut so the piece curls slightly.