Heat the oil in a large saucepan over medium-high heat. Add the carrots, onion, and poblano and cook, stirring, for 3 minutes. Add the beef and cook, breaking it up with a spoon, until it is no longer pink, 3 to 5 minutes.
Add the tomato paste and cook, stirring, until it is slightly darkened, 1 minute. Add the beans, chili powder, 3 cups water, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Simmer over medium heat until the vegetables are tender, about 10 minutes.
Stir in the corn. Divide among bowls and top with the Cheddar and scallions.
Make Ahead: You can cook the chili in advance and refrigerate it for up to 3 days or freeze it for up to 3 months.