Place broth in a medium sauce pan and heat to a simmer; reduce heat and keep warm.
Clean and chop 2 cups mushrooms. Remove the stems from the kale and chop the leaves. Mince 1 shallot.
In a large heavy-bottomed skillet, pot or Dutch oven, heat 2½ tablespoons butter over medium high heat. Add the shallot, mushrooms, kale, and ½ teaspoon kosher salt, reduce heat to medium, and cook until the shallots are translucent, stirring often, about 3 minutes. Add 1½ cups Arborio rice and stir to combine; cook for 2 minutes. Increase heat to medium-high and add ¾ cup white wine. Cook, stirring, until liquid is almost evaporated, a few minutes.
At this point, you’re ready to start adding the broth. Add ½ cup warmed broth to skillet. Cook, stirring frequently, until broth is almost absorbed. Repeat, gradually adding broth ½ cup at a time and stirring, until rice is tender but still al dente and sauce is creamy (you may not need all the broth). The process should take about 20 to 25 minutes.
Stir in ¾ cup Parmigiano-Reggiano cheese. Continue to stir until combined (or turn off the heat and cover the dish for a few minutes). Remove from heat and season to taste with kosher salt and pepper. Serve immediately, garnished with Parmigiano-Reggiano cheese.