For the piquillo pepper pesto: Combine the piquillo peppers, Parmesan, pine nuts, garlic, honey and red chile flakes in a food processor and process. While processing, drizzle in enough oil to create an emulsified sauce. Season with salt and pepper. Reserve.
For the tapenade: Combine the olives, anchovies and garlic in a food processor and process. While processing, drizzle in enough oil to create an emulsified sauce.
For the mashed potatoes: Put the potatoes in a pot, cover with cold salted water and bring to a boil over medium-high heat. Cook until fork-tender, 5 to 7 minutes.
In a separate saucepan heat up the milk.
Drain the potatoes well to remove any excess water. Using a ricer, mash the potatoes into a mixing bowl while they are hot. Add the butter, mascarpone and a splash of the hot milk and fold into the potatoes until incorporated. Add just enough milk to achieve a velvety consistency. Season with salt and pepper. To keep warm until serving, place the bowl over a pot of simmering water.
For the bison: Preheat the broiler on high.
Place a large saute pan on high heat and add enough oil to coat the bottom of the pan. Sprinkle both sides of the bison tenderloins well with salt and pepper and place on the smoking-hot pan to sear. Once a crust has formed on the bottom, remove the meat from the pan and slice it. Return the slices to the pan. Spread the slabs of butter on top of the meat. Season with a little more salt and pepper and place under the broiler until the butter is melted.
Put the arugula in a bowl, drizzle with extra-virgin oil and toss together. Season with salt and pepper.
To assemble: Barely fold 2 tablespoons of the tapenade into the potatoes. Place several pieces of the bison on each plate and top with a dollop of the piquillo pepper pesto. Spoon some of the pan butter sauce over the bison and garnish with some arugula. Put a scoop of the tapenade-marbled potatoes next to the bison and garnish with minced chives.