Heat the oil in a large lidded skillet over medium heat until shimmering. Add the shallot and cook, stirring occasionally, until translucent, 3 to 5 minutes. Stir in the garlic, nutritional yeast, oregano, salt, and black pepper and continue to cook, stirring occasionally, until fragrant, 2 to 3 minutes.
Add the tomatoes and beans, cover, and cook for 5 minutes, stirring halfway through to prevent sticking. Add the kale and basil and cook, stirring constantly, until wilted, 1 to 2 minutes. Stir in the coconut milk and, if needed, season with more salt. Garnish with chopped basil and serve.
