Bring a large pot of salted water to a boil
In a wide, deep skillet, heat the oil over medium-high. Add the chickpeas, rosemary, Aleppo pepper, and red pepper flakes. Season with salt and pepper to taste. Cook, stirring occasionally, until chickpeas start to caramelize at the edges and pop, about 5-7 minutes. Using a slotted spoon, transfer about half of the chickpeas to a bowl and reserve for garnish
Reduce heat to medium and add shallots and garlic to the skillet; season with salt and pepper. Cook, stirring occasionally, until shallots are softened - about 3 minutes. Add heavy cream and cook until slightly thickened, about 3 minutes. Turn off the heat, stir in the spinach, and season to taste with salt and pepper
Add the pasta to the boiling water and cook until al dente or a couple of minutes short. Do not drain the pasta - using tongs, transfer it to the cream sauce. Add 1 cup of pasta cooking water to the sauce and add the Parmesan; toss with tongs until sauce is thickened and noodles are fully cooked, about 3 minutes. Add a splash of pasta water to loosen the sauce as needed
Transfer to bowls and garnish with reserved chickpeas, rosemary, and black pepper