In a large pot or Dutch oven, heat the oil over medium heat. Once hot, add the onions, leeks, garlic, oregano, pepper, and salt. Sauté, stirring occasionally, until the onions and leeks are translucent, about 5-7 minutes.
Add in the miso and stir to combine until it melts into the veggies. Pour in the wine, stir, and cook until the wine has reduced by half, about 2 minutes.
Add in the vegetable stock, thyme sprigs, and cheese rind. Turn the heat up to medium-high and bring to a simmer. Cover with a tight-fitting lid, and turn down to low. Cook for about 25 minutes to allow the parmesan and thyme to infuse into the broth.
After the soup has simmered, remove thyme and parmesan cheese rind. Turn the heat back up to medium, and add in the peas, kale, and cannellini beans.
Simmer uncovered for 5 minutes until the peas are bright green and the kale has softened slightly. Remove from the heat and stir in half of the dill, the lemon zest, and lemon juice.