Heat the broth in a small pot over low heat or in the microwave until steamy.
Place a large sauté pan over medium heat and add in the butter or oil along with the shallots. Season with salt and pepper and cook, stirring frequently, until softened and lightly golden, about 2 to 3 minutes. Add in the garlic, orzo, and red pepper flakes and cook, stirring frequently, for 1 minute to toast the pasta and cook off the garlic.
Turn the heat down to medium-low and pour in the white wine. Cook down, stirring frequently, until almost all the wine has been absorbed then begin adding the hot broth, about ½ cup at a time, stirring after each addition and letting it absorb before adding more.
Stir through the lemon zest and lemon juice along with the baby spinach and Parmigiano Reggiano. Allow the cheese to melt in and the spinach to wilt. Finish the orzotto with the cream and fresh parsley and season to taste with more salt, pepper, cheese, and/or lemon, if needed.