Preheat the oven to 350 degrees F.
Cut the top third of the garlic off and discard. Place the garlic head into a piece of foil and sprinkle with salt and pepper. Add some olive oil and enclose in the foil. Put into the oven and roast until golden and tender, 30 to 35 minutes.
Increase the oven to 375 degrees F.
Place the poblano on a sheet pan and into the oven. Roast, about 25 minutes. Remove the poblano from the oven and place into a bowl. Cover with plastic wrap and allow to steam, about 10 minutes. Peel, stem, seed and dice the poblano. Set aside.
Place the diced potatoes into a pot and cover with water. Season the water with salt and turn the heat to medium-high. Cook until tender, and then drain.
To a cast-iron pan over medium-high heat, add the butter, canola oil and shallots. Allow the shallots to sweat, 2 to 3 minutes. Add the drained potatoes in one layer and allow them to crust and brown, about 5 minutes. Add the poblano and piquillo peppers. Smash 2 of the roasted garlic cloves and toss to combine. Add the cilantro and toss to combine. Taste and season if necessary.