To a large pot, add the olive oil, grape tomatoes, thyme (be sure to remove the stems first), ginger, salt, pepper, brown sugar, onions, garlic, celery, and leek. Sauté over medium-high heat (see notes) for 5 minutes.
While the vegetables are sautéing, peel and cube the sweet potatoes, then add them to the pot alongside the vegetable broth. Bring to a boil over high heat (see notes), which will take about 5 minutes. Meanwhile, thoroughly wash the cabbage, cut off the end, then chop it and add it to the pot.
Lower the heat to medium, add a lid and cook for 10 minutes. During those 10 minutes, rinse and drain the canned beans, prepare the kale and juice the lemon.
Add the kale, beans, and lemon juice to the pot, lower the heat to medium-low and simmer for 5 more minutes.
Serving Suggestion & Storage: serve as is or with a slice of lemon and some freshly cracked pepper, as well as sliced sourdough bread. Let leftovers cool, then transfer them to an airtight container and store in the fridge for up to 3 days.