Brussels Sprouts with Walnuts

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2 tablespoons minced garlic

3/4 cup roughly chopped walnuts

2 teaspoons fresh lemon juice

1 teaspoon salt

1/4 teaspoon freshly ground black pepper

1/2 cup finely grated Parmesan

2 pounds Brussels sprouts, base and outer leaves trimmed, and halved

8 tablespoons unsalted butter

1/4 cup thinly sliced shallots