In a large pot, heat 1 tablespoon of the olive oil over medium-high heat. Add the onion, bell pepper, and carrot and cook, stirring occasionally, until tender and lightly browned, about 15 to 20 minutes.
While the vegetables cook, prepare the tempeh. Place the tempeh in a large skillet and add enough water to almost cover it. Add the soy sauce and bring to a boil over high heat. Let simmer, stirring occasionally, until the water is absorbed, about 15 minutes. Using a fork, mash the tempeh into crumbles — chunky, not paste. Add the remaining 2 teaspoons of olive oil and sauté over medium heat for about 15 more minutes, until the tempeh is nicely browned.
When the vegetables are ready, add the garlic and stir for 30 seconds. Add the salt, chili powder, cumin, oregano, and black pepper and stir for another minute. Pour in the beer and scrape up any bits from the bottom of the pot. Let cook for 2 minutes.
Add the diced tomatoes, tomato paste, beans, broth, and cooked tempeh. Stir everything together, reduce heat to medium, cover, and cook for 20 minutes, stirring occasionally. Uncover and cook for another 30 minutes, stirring occasionally, until the chili is thick and deeply flavored.
Stir in the maple syrup and lemon juice. Taste and adjust salt if needed. Add the cilantro, stir, and serve.