Heat the oil over medium heat in a large pot or dutch oven. Add the chicken sausage and cook, breaking up and stirring occasionally until fully cooked, 5 to 7 minutes. Remove from the pot and set aside.
In the same pot, add the diced onion and cook, stirring often until translucent, 3 to 4 minutes. Stir in the garlic, basil, oregano, salt, pepper, and red pepper flakes. Cook, stirring constantly until fragrant, 1 to 2 minutes.
Stir in the chicken broth, beans, and crushed tomatoes. Cover the pot and bring to a boil, then reduce to a simmer and cook, covered, for about 10 minutes to soften the beans. Carefully remove 2 cups of the soup and transfer to a blender. Blend with the steam vent open, on high speed until completely smooth. Pour back into the pot and stir to combine.
Add the tortellini and cover again. Simmer until the tortellini rises to the top, about 3 minutes. Add back the chicken sausage and stir in the kale. Let it wilt down for 2 to 3 minutes, then serve with nutritional yeast or grated parmesan on top.