In a large saucepan, stir together the oil and popcorn kernels. Cover and cook over medium heat just until you hear the kernels begin to pop, 3 to 5 minutes. Tilt the lid slightly, allowing steam to escape. Cook until the popping slows, about 2 minutes. Remove from the heat and let stand until the popping stops, about 30 seconds.
Preheat the oven to 300 degrees F. Spread slivered almonds and shredded coconut on a parchment-lined baking sheet. Bake until just barely brown, about 10 minutes; let cool. Mix the almonds, coconut, white chocolate chips and salt with warm popcorn.