For the dressing: Whisk together the mayonnaise, vinegar, mustard and garlic in a bowl and season with salt and black pepper. Let sit while the potatoes boil to allow the flavors to meld.
For the salad: Preheat the oven to 375 degrees F. Toss the poblanos with a few tablespoons of canola oil and sprinkle with salt and black pepper. Put the poblanos on a baking sheet and roast until the skin is blackened on all sides, turning a few times, about 25 minutes. Transfer to a bowl and immediately cover with plastic wrap. Let sit and steam for at least 15 minutes and up to a few hours. Transfer to a cutting board and remove the skin and seeds. Thinly slice the poblanos and set aside.
While the chiles are roasting, put the potatoes in a large saucepan and cover by 2 inches of cold water. Add 2 tablespoons salt to the water and bring to a boil over high heat. Cook until a skewer or paring knife inserted into the center of the potatoes meets no resistance, about 25 minutes (depending on the size of the potatoes). Drain and let cool for at least 5 minutes on a cutting board. Cut the potatoes into 1-inch dice.
Heat 3 tablespoons canola oil in a large cast-iron skillet over high heat until the oil begins to shimmer. Add the potatoes in a single layer and cook, pressing firmly with a spatula, until a crust has formed on the bottom. Gently turn them and cook until all sides are golden brown and crisp, adding more oil if needed. Transfer the potatoes to a bowl, and then add the chiles, radicchio and dressing and stir gently to combine. Fold in the cilantro and green onions and serve warm or at room temperature.