Drizzle oil into a pan over high heat. Add beef chuck. Cook and stir until juices evaporate and the beef starts to brown and stick to the bottom of the pan, 5 to 7 minutes. Add butter and reduce heat to medium; stir until butter is melted.
Add onions, salt, pepper, and cayenne to the beef. Cook until onions are softened and golden, 2 to 3 minutes. Stir in flour. Cook and stir until flour smells like cooked pie crust, 2 to 3 minutes. Pour in broth and bring to a simmer over high heat. Bring heat back down to medium. Let simmer, uncovered, until gravy reaches your desired thickness, 15 to 20 minutes, scraping down the sides occasionally. Season with salt.
Preheat the oven to 450 degrees F (230 degrees C). Lay fries out on a baking sheet.
Bake in the preheated oven, turning halfway, until crispy and golden brown, 13 to 18 minutes.
Fill a serving platter with fries. Scatter cheese curds on top. Ladle a portion of the beef gravy on top and garnish with chives.