Heat the olive oil in a large pot over medium-high heat. Add the garlic and onions and cook, stirring, for 3 to 4 minutes. Add the tomato paste and cook, stirring, about 2 minutes, getting lots of flavor in the bottom of the pot. Stir in the red pepper flakes and dried oregano; cook and stir for another 30 seconds.
Pour in the wine and whisk, scraping the bottom of the pot a bit as you go. Allow this to bubble up and reduce, cooking until the wine is reduced by half, about 10 minutes. Add the canned tomatoes, then the beans. Pour in the chicken broth. Stir to combine, bring to a simmer and simmer for 20 to 25 minutes. Sprinkle in salt and pepper to taste.
Rinse the kale and tear it into chunks. Stir it into the soup (it'll shrink quite a bit, so don't be afraid when you first add it!). Simmer the soup for another 5 minutes, tasting and adding salt and pepper (or even more red pepper flakes) as needed.
Transfer the soup to a large serving bowl. Add big, fat Parmesan shavings and garnish with torn basil.