Make the ragù: Heat oil in a 6-qt. saucepan over medium-high. Cook pork and bacon until browned, 4–5 minutes. Add chile flakes, fennel pollen, and garlic; cook until garlic is golden, 2–3 minutes. Stir in tomato paste; cook 2 minutes. Add wine; cook until evaporated, about 30 seconds. Add 4 cups stock and season with salt; boil. Reduce heat to medium; simmer until thickened, about 1 hour.
Make the gnocchi: Boil potatoes in a 4-qt. saucepan of water. Reduce heat to medium-high; simmer until potatoes are tender, 25–30 minutes, and drain. When cool enough to handle, peel and pass through a potato ricer into a bowl. Add flours, parmesan, and eggs; using your hands, mix until a soft dough forms. Transfer dough to a lightly floured surface; knead briefly until dough is smooth. Cover dough with plastic wrap; let sit at room temperature for 30 minutes.
Quarter dough and, working with one quarter at a time, use your hands to roll the dough into a 1⁄2"-thick rope. Cut rope crosswise into 1" gnocchi; transfer gnocchi to a semolina-dusted, parchment paper-lined baking sheet. Separate gnocchi to prevent sticking.
Bring a large pot of generously salted water to a simmer over medium-high. Cook gnocchi, all at once, until they float, 2–3 minutes. Using a slotted spoon, transfer gnocchi to a parchment paper-lined baking sheet; keep warm. Return ragù to medium. Add remaining stock and the butter; simmer until sauce is thickened, 6–8 minutes. Add cooked gnocchi and the parmesan; cook until warmed through, 1–2 minutes. Divide gnocchi and sauce between shallow bowls; garnish with more parmesan and parsley.