Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef and cook, breaking up the meat, until browned, about 3 minutes. Add the onion, poblano and garlic; cook, stirring occasionally, until the vegetables are tender and lightly browned, about 5 minutes. Stir in the chili powder, cumin, 1 teaspoon salt and a few grinds of pepper. Cook, stirring, until combined, about 1 minute.
Add the tomatoes and the beans and their liquid to the pot; bring to a boil, then reduce the heat to medium and simmer until the liquid is slightly reduced, about 5 minutes.
Stir the squash into the pot. Partially cover and cook, stirring occasionally, until the squash is tender and the chili thickens slightly, about 10 minutes (add up to ½ cup water if the chili is too thick). Season with salt. Top each serving of chili with the avocado and some cilantro.