Heat a large pot over medium heat, add enough olive oil to lightly coat the bottom. Add the corn kernels and a pinch of salt. Saute until the corn is bright yellow and slightly caramelized, about 7 minutes. Transfer to a small bowl and set aside.
Add more oil to coat the bottom of the pot. Add the onion and a pinch of salt, saute for 7 minutes, until translucent. Add the garlic, paprika, thyme, and black pepper to taste, saute for 1 more minute, until fragrant. Add the wine, bring it up to a simmer and let reduce for 5 minutes. Add the reserved corn cobs to the pot, along with the bay leaves, 6 cups of water, and more salt. Increase the heat to high, cover the pot, and bring to a boil. Lower the heat to a simmer and simmer, covered, for 30 minutes. Remove the corn cobs and bay leaves from the broth, discard. Add the broccoli and cashews to the pot, bring it back up to a simmer, and simmer, covered, for another 5-7 minutes, until the broccoli is tender.