Set up a large pot or popcorn popper on medium heat. Add a few kernels and cover; once they pop, add the rest of the popcorn kernels. Shake the pot gently while popping to prevent burning. Continue until popping slows to a stop, then remove from heat and transfer the popped popcorn to a large bowl.
Melt the unsalted butter in a microwave-safe bowl or double boiler, stirring until smooth. Once melted, stir in the milk (if using) and half of the shredded cheddar cheese, mixing until the cheese begins to melt and the mixture is creamy. Add the smoked paprika and salt, then stir to combine evenly.
½ cup popcorn kernels
Slowly pour the cheese mixture over the warm popcorn, using a spatula or large spoon to toss and coat the kernels evenly. Continue until most of the popcorn is covered with the cheesy mixture and the cheese has melted further, creating a glossy, fragrant coating.
½ cup popcorn kernels
Sprinkle the remaining shredded cheddar cheese and extra smoked paprika over the coated popcorn, tossing gently to distribute evenly. Look for a vibrant, cheesy appearance with visible specks of paprika clinging to the popcorn.
½ cup popcorn kernels
Spread the popcorn onto a baking sheet lined with parchment paper. Bake in a preheated oven at 350°F (175°C) for 5-7 minutes, just until the cheese is bubbling and slightly golden around the edges. Remove and let cool for a few minutes before serving.
Serve the popcorn in a large bowl, showcasing its crispy, cheesy appearance with flecks of paprika and a rich, savory aroma. Enjoy immediately for the best crunch and flavor.