Soak the cut potatoes in cold water for 20-30 minutes, then dry thoroughly. I found that removing surface starch prevents sticking and improves crisping.
Heat oil to 130°C (266°F) for the first blanch fry. Fry potatoes in batches for 4-5 minutes until soft but pale. Drain on a rack. This gentle blanch sets the interior starch without excessive browning.
Increase oil to 180°C (356°F). Fry blanched potatoes in batches for 2-3 minutes until golden brown and crisp. Notice how the exterior forms a rigid crust while the interior stays tender.
While fries finish, melt butter in a skillet over medium heat. Add sliced onions and a pinch of salt. Cook, stirring, for 8-12 minutes until deep golden and jammy. The onion sugars break down; you should smell sweet, caramel aromas.
Make the animal sauce: whisk mayonnaise, ketchup, relish, mustard, 1/4 tsp salt, and a pinch of pepper until smooth. Taste and adjust acid-sweet balance; the emulsion should be glossy and slightly tangy.
Pile hot fries on a serving tray, layer shredded cheese over them, then spoon hot grilled onions on top. The residual heat melts the cheese; if needed, pop under a broiler for 30-60 seconds to achieve a gooey finish.
Drizzle the animal sauce over the piled fries, season with extra salt if needed, and serve immediately. Notice the contrast between the crisp fry, molten cheese, and silky sauce with sweet onion hits.