To prepare gnocchi: Line a large rimmed baking sheet with parchment paper and generously dust with semolina flour.

Drain ricotta and pat dry with paper towels. Combine the ricotta, grated Parmesan and 1/2 teaspoon salt in a large bowl; add 3/4 cup flour and stir until just combined. Whisk egg and egg yolk in a small bowl and stir into the ricotta mixture until loosely combined. Generously dust a work surface with all-purpose flour and turn the dough out onto it. Gently knead the dough with floured hands; if it seems very wet and sticky, work in more flour, 2 tablespoons at a time, gently folding it over and continuing to dust the surface underneath until you're able to form it into a 3-by-6-inch log.

With a floured knife, cut the log crosswise into 4 equal pieces. Starting at the center of the dough and pressing lightly with your fingers, roll each portion into a 3/4-by-15-inch rope, gently pulling and stretching the dough as you roll. Cut into 1/2-inch pieces and place on the prepared baking sheet. Place in the freezer until the gnocchi are frozen, about 30 minutes. (If making ahead, transfer to a sealable bag once frozen. Do not defrost before boiling.)

To prepare sauce: If using fresh fava beans, bring a medium saucepan of water to a boil. Add the shelled beans and cook for 30 seconds. Drain well. Remove the "cap" at the top and slip each bean out of its waxy coating.

Heat oil in a large skillet over medium-low heat. Add leeks and cook, stirring occasionally, until very soft, 6 to 8 minutes. Stir in asparagus, peas and the favas (or lima beans). Add broth, 1/2 teaspoon salt and pepper. Bring to a boil over high heat. Cook, stirring often, until the asparagus is almost tender, about 2 minutes. Remove from heat and set aside.

To cook gnocchi: Bring a large pot of water to a boil. Add the remaining 1 teaspoon salt and drop in the frozen gnocchi. Cook, stirring gently, for 4 to 5 minutes. As the gnocchi float to the top, scoop them into a large bowl with a slotted spoon.

Reheat the sauce, if necessary, and stir in butter, basil (or tarragon) and parsley. Pour the sauce over the gnocchi; gently stir to combine. Serve topped with shaved Parmesan.