Coat the bottom of a large saucepan with 1 tablespoon of olive oil and place over medium heat. When oil is hot, add mushroom slices in an even layer. Allow to cook for 5 minutes, until browned on bottoms, flip and cook 5 minutes more. Remove from pot and transfer to a plate.
Coat the bottom of the pot with remaining tablespoon of olive oil and add onion. Sauté until softened, about 5 minutes. Add rice and continue to sauté until it begins to turn translucent, about 2 minutes. Add wine and bring to a simmer. Allow to cook until most of the wine has been absorbed or evaporated, about 2 minutes, stirring frequently.
Add ½ cup of broth and bring to a simmer. Allow to simmer, stirring frequently until broth is almost fully absorbed. Continue adding ½ cup of broth at a time in this manner, stirring every minute or two, until rice is plump and tender, adding kale pesto mixture and mushrooms with the last broth addition. This should take about 25-30 minutes. Stir in cashew milk and continue to simmer until thick and creamy, 2-3 minutes.
Remove from heat and season with salt and pepper to taste. Serve.