In a 5- to 6-qt. pot (preferably wide), heat oil over medium heat. Add onions, garlic, mushrooms, carrots, jalapeños, and salt. Cover and cook until vegetables get juicy, 5 to 8 minutes. Uncover and cook, stirring often, until mixture begins to brown, 10 to 15 minutes more.
Add chili powder and cumin; stir until fragrant, about 1 minute. Stir in broth, beans, tomatoes, and tomato sauce and bring to a simmer. Add more salt to taste and simmer to heat through and combine flavors, about 10 minutes.
Ladle chili into wide bowls and serve with your favorite toppings.
Wine pairing: Sbragia Family 2012 Home Ranch Merlot (Dry Creek Valley; $32).