Prepare the pesto: combine all ingredients except the olive oil in a food processor or blender and process until the basil and kale are in very small pieces. Scrape the sides, then slowly stream in the olive oil while continuing to process on low speed, until fully incorporated. Scrape down the sides and process as needed until even in texture. Measure out ¼ cup of the prepared pesto, set aside, and store the rest in an airtight container in the refrigerator.
Heat the olive oil in a large pot or dutch oven with a lid over medium heat. Once the oil is shimmering, add the shallot and cook until translucent, 1 to 2 minutes.
Add the garlic, oregano, salt, black pepper, and red pepper flakes and continue cooking, stirring constantly, for another minute. Incorporate the nutritional yeast and stir again.
Add the rice and stir to coat in the spices. Let the rice toast while stirring constantly for 1 to 2 minutes. Pour in the broth, water, and coconut milk, cover the pot, increase the heat to medium high and bring to a boil. Once boiling, reduce the heat to medium low and cook, covered, until the rice is just about fully cooked, 9 to 12 minutes.
Add the beans and kale to the pot, stir to combine, and cook, covered, for 3 to 5 minutes to soften the beans and kale and finish cooking the rice. Note: you can add additional water here to thin as needed.
Remove the lid and stir in the basil, pesto, lemon juice, and lemon zest. Salt to taste and simmer on low to let the flavors combine for about 5 minutes, then serve.
