Preheat the oven to 325 degrees. Butter an 8-inch square baking pan. Line the bottom and two sides with parchment paper.

In a large saucepan, melt the butter with the honey and sugar and cook over moderate heat, stirring constantly, until an amber caramel forms, about 5 minutes. Stir in the oats, pine nuts, pepper and salt and cook, stirring constantly, until the pine nuts just begin to brown, about 2 minutes. Scrape the mixture into the prepared pan and smooth the surface. Bake for about 20 minutes, until bubbling and browned around the edges. Let the bars cool completely in the pan.

Run the tip of a knife around the edge of the pan and lift the square from the pan. Cut the square in half, then cut each half into 6 bars. Discard the parchment paper.

Line a baking sheet with parchment paper. In a microwave-safe bowl, melt the white chocolate at high power at 30-second intervals, stirring in between. Stir in the oil and let cool slightly. Dip the bottom half of each oat bar into the white chocolate and set the bars on the baking sheet. Refrigerate just until the white chocolate is set. If the chocolate looks thin, dip the bars a second time.

The bars can be refrigerated for 1 week or kept at room temperature for up to 3 days.