Roast the poblano peppers over a gas burner or under the broiler, turning frequently, until the skins are fully blackened and blistered. Transfer to a sealed bag or covered bowl and let them steam for at least 15 minutes.
Add diced bacon to a large, cold pot and bring to medium-low heat. Cook for 5 minutes until the fat renders and the bacon begins to crisp.
Add the olive oil and stir to combine. Sprinkle the cornmeal over the mixture and stir to coat. Let it toast for 30 to 60 seconds.
Begin adding chicken stock slowly, starting with 1/4 cup and stirring between each addition until the cornmeal is fully hydrated and smooth. Once a few cups are incorporated, add the remaining stock and bring to a gentle simmer. Simmer for 10 minutes.
Peel the skins off the rested poblano peppers. Remove the stems and seeds. Do not rinse.
Add the roasted poblanos and softened cream cheese to the pot. Turn off the heat and let it sit for 10 to 15 minutes.
Remove bay leaves. Blend completely smooth using an immersion blender or working in careful batches in a countertop blender.
Return to low heat and bring back to a gentle simmer. Taste and adjust salt and pepper.
Add corn kernels, shredded chicken, and cubed potatoes. Stir to combine. Cover with the lid slightly ajar and simmer on low for 30 minutes, until potatoes are fork tender.