Using a vegetable peeler or cheese grater, shred 1/2 cup Parmesan cheese and set it aside. Reserve the rind.
In a large heavy-bottomed stock pot set over medium-low heat, add the olive oil and onions. Cook, stirring occasionally, until the onions are translucent, about 5 minutes.
Add the Brussels sprouts and garlic, and cook, stirring occasionally, until softened, about 5 minutes.
Add the chicken stock and Parmesan cheese rind. Bring the mixture to a boil then reduce it to a simmer. Add the tortellini and cook until the tortellini are tender, about 7 minutes.
Turn off the heat then immediately stir in the kale lemon juice. Taste and season the soup with salt and pepper. (If the Parmesan rind hasn’t fully melted, discard it from the soup.)
Divide the soup into serving bowls. Garnish with reserved Parmesan cheese and pesto.
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