Smashed Root Vegetables

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3 parsnips, peeled, cut into 1-inch pieces (about 2 1/4 cups)

2 cloves garlic, smashed 

2 Yukon Gold potatoes, peeled, cut into 1-inch cubes (about 2 cups) 

1 celery root, peeled, cut into 1-inch cubes (about 2 cups) 

1 teaspoon kosher salt, plus 2 tablespoons for the cooking water 

Zest of 1 small lemon 

1/2 teaspoon chopped fresh thyme 

1/4 cup extra-virgin olive oil 

1/4 cup freshly grated Parmesan