Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 cup cooking water, then put the peas in a colander and drain the pasta over the peas.
Place the empty pot over medium heat and add the butter, swirling to melt. Add the radishes, shallot and red pepper flakes. Cook, stirring occasionally, until the radishes are slightly softened, about 2 minutes. Add the pasta and peas along with the spinach, herbs, lemon juice, 3/4 cup reserved cooking water, 1/2 teaspoon salt and a few grinds of pepper. Cook, tossing, until the spinach is wilted and the pasta is lightly coated, gradually adding more of the reserved cooking water if needed.
Mix the ricotta, lemon zest, 1/4 teaspoon salt and a few grinds of pepper in a small bowl. Serve over the pasta.