Porcini and Truffle Crescent Rolls

Name: Porcini and Truffle Crescent Rolls
Ingredients: 2½ cups (12½ ounces/354 grams) all-purpose flour; 1 ounce (28 grams) dried porcini mushrooms , rinsed and minced; 4 teaspoons minced fresh thyme; 1 teaspoon instant or rapid-rise yeast; 1 teaspoon table salt; 1 large egg plus 1 large yolk, room temperature, plus 1 large egg beaten with 1 teaspoon water; ½ cup half-and-half , room temperature; 7 tablespoons unsalted butter , melted and cooled slightly; ¼ cup (1¾ ounces/50 grams) sugar; 5 teaspoons truffle oil , divided