Asparagus and mushroom salad with creamy Grana Padano vinaigrette

2 tablespoons sour cream

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1 tablespoon balsamic vinegar

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2 teaspoons fresh thyme leaves

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2 tablespoons olive oil, divided

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3/4 cup Grana Padano cheese curls, divided

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Salt, as needed

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Pepper, as needed

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3/4 pound mixed mushrooms, trimmed and sliced thick

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3 tablespoons minced shallot

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1 garlic clove, minced

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1 pound thin asparagus, trimmed and cut into 2-inch pieces

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4 large leaves Boston lettuce