For the white chocolate cream: Bring 1 inch of water to a simmer in a medium pot. Combine the cream, butter, corn syrup and white chocolate in a heatproof bowl that will sit on top of the pot (don't let the bottom of the bowl touch the water). Cook, stirring, until melted and smooth. Cool to room temperature.
For the caramel sauce: Stir the sugar, corn syrup and honey with 1/2 cup water in a medium pot. Bring to a boil, without stirring. Continue to cook until amber in color, swirling the pot a few times once it starts to brown, about 15 minutes. Slowly pour in the cream and, when the bubbling subsides, whisk until smooth. Remove from the heat and cool to room temperature.
For the pecans: Preheat the oven to 350 degrees F. Toss the pecans with the oil and salt and spread on a small, rimmed baking sheet. Bake, stirring once or twice, until toasted, 8 minutes. Cool and then finely chop.
To build the ice cream, soften the ice cream at room temperature until workable but not melting. Scrape into a large metal bowl. Add the white chocolate cream and the pecans and work into the ice cream until well distributed. Drizzle with the dark creme de cacao. If needed, return the ice cream to the freezer until firm enough to stir without melting. Drop spoonfuls of the caramel over the ice cream and stir once or twice to create a chunky ribbon.
Cover the bowl with plastic wrap and put in the freezer until firm, at least 3 hours or overnight. Serve in a cone or a dish.