To make the pesto. Heat 2 tablespoons olive oil in a large skillet over medium heat. When the oil shimmers, add the sage and cook 2 minutes, until fragrant and crisp. Remove from heat. In a food processor, pulse together the remaining 1/3 cup olive oil, kale, pistachios, and parmesan until finely chopped. Add the sage and season to taste with salt and crushed red pepper flakes, pulse to combine. Make the soup. Heat the olive oil in a large pot over medium heat. When the oil shimmers, add the shallots and cook until soft, about 5 minutes. Add the thyme and butter, cook another 30 seconds. Pour in the broth. Add the sweet potatoes, cayenne, nutmeg, and a pinch each of salt and pepper. Bring the soup to a boil over medium-high heat and then reduce the heat to medium-low. Cover and simmer for 15 to 20 minutes, until the potatoes are fork-tender.Using an immersion blender, blend the soup directly in the pot until smooth. Stir in the coconut milk and 2 tablespoons sage pesto, cook another 5 minutes. If the soup is thick, thin with addition broth.To serve, ladle the soup into bowls. Swirl each bowl of soup with pesto. Break the burrata and spoon some over top the soup. Enjoy!