Heat the oil in a large heavy pot (at least 6 litres) over medium heat.
Add the onion and peppers and cook, stirring, until soft, about 6 minutes.
Turn the heat to medium-high, add the turkey and garlic and break the meat up with a wooden spoon. Cook until no pink remains and it reaches 74°C (165°F), about 8 minutes.
Stir in the chili powder, cumin, smoked paprika and oregano for 1 minute, then add the diced and crushed tomatoes and the drained beans.
Bring to a boil, then lower the heat to low and simmer partly covered for 25 minutes, stirring every 5 to 10 minutes so the bottom does not scorch.
Season with the salt and serve topped with grated cheddar and green onion. Cool leftovers within 2 hours; keeps 4 days in the fridge or 3 months frozen.
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Tips
Chili is better the next day; make it ahead.
Swaps
Dairy-free: skip the cheese and add avocado.
Vegetarian: replace the turkey with two more cans of beans and a bag of frozen corn.