Heat oven to 375˚F. Oil a 2-quart baking dish. Bring a large pot of salted water to a boil. Add the beans and cook until just tender, 3 to 4 minutes. Drain and run under cold water to cool.

Meanwhile, heat 1 tablespoon oil in a large skillet over medium heat. Add the sausage and cook, breaking it up with a spoon, until browned, about 5 minutes. Transfer to a bowl and toss with the breadcrumbs and 2 tablespoons Parmesan.
Wipe out the skillet and warmth the remaining 2 tablespoons oil over medium heat. Add the onion, season with 1/2 teaspoon salt and 1/4 teaspoon pepper and cook, covered, stirring sometimes, until very tender, 6 to 8 minutes. Stir in the garlic and cook for 1 minute.

Whisk in the milk and bring to a simmer. Whisk in the cream cheese, nutmeg, cayenne, and remaining 1/4 cup Parmesan and simmer, stirring sometimes, until barely thickened, 2 to 3 minutes; stir in the lemon zest and toss with the green beans.

Fold in the spinach and transfer to the prepared baking dish. Sprinkle with the sausage mixture and bake until golden brown, 15 to 20 minutes.