Reduce the heat to medium-low. Add the shallots, garlic, and red pepper flakes. Cook, being careful not to burn, until the shallot begins to soften, about 2 minutes.
Add the sun-dried tomatoes and wine. Cook, stirring, scraping up bits until the wine is reduced by half.
Add the pasta, chicken broth, milk, salt, and Italian seasoning. Bring to a gentle simmer and cook, stirring often, until the pasta is al dente and the liquid is absorbed and creamy, 12 to 15 minutes. If your pasta is still not done, you may need to add 1/4 cup more liquid and continue to cook until al dente and the sauce is creamy.
Reduce the heat to low. Stir in the lemon and spinach, two cups at a time, until wilted down. Add the pepper and Parmigiano-Reggiano and continue to stir until the cheese is melted and combined.
Divide the pasta amongst 4 bowls. Garnish with more Parmigiano-Reggiano and fresh parsley, if desired.