Mushroom and Ajwain Pissaladière

Name: Mushroom and Ajwain Pissaladière
Ingredients: 1 sheet frozen puff pastry, thawed according to package directions; olive or canola oil; 3 tablespoons unsalted butter; 2 ½ cups sliced mixed mushrooms (I used a mixture of cremini, shiitake and oysters); ¼ teaspoons ajwain seeds; ¼ teaspoons cumin seeds; 2 medium-sized Spanish onions, thinly sliced; ¼ teaspoons crushed red pepper; scant ½ teaspoons black pepper; scant ½ teaspoons chili powder; scant ½ teaspoons ground cumin; 1 egg; 1 tablespoon water; fresh thyme leaves; salt