Grilled Artichoke and Celery Root Puree

Name: Grilled Artichoke and Celery Root Puree
Ingredients: Two 10-ounce celery roots (celeriac), ends trimmed, peeled and cut into 1-inch pieces; 2 tablespoons unsalted butter, at room temperature; 1 tablespoon kosher salt; 1 pound frozen artichoke hearts, thawed; 1/3 cup extra-virgin olive oil; 2 cloves garlic, minced; 1 tablespoon chopped fresh thyme; 1 teaspoon kosher salt; 1/2 teaspoon freshly ground black pepper; 2/3 to 1 cup whole milk, at room temperature; 1 tablespoon unsalted butter, at room temperature