In a 6-quart saucepan over medium heat, heat the olive oil. Add the onions and poblanos and a heavy pinch of salt and sweat for 10 minutes. Add the potatoes and the vegetable broth, increase the heat to medium-high, and bring to a boil. Reduce the heat to low and simmer until the potatoes are soft, approximately 30 minutes.
Turn off the heat and puree the mixture with an immersion blender until smooth. Stir in the half-and-half, buttermilk, salt and pepper.