Mushroom and Ajwain Pissaladière Recipe

Name: Mushroom and Ajwain Pissaladière Recipe
Ingredients: 2 tablespoons olive or canola oil, plus more as needed; 3 tablespoons unsalted butter; 2 1/2 cups mixed mushrooms (such as cremini, shiitake, and oyster), sliced; Salt, to taste; 1/4 teaspoon ajwain seeds*; 1/4 teaspoon cumin seeds; 2-3 medium-sized Spanish onions, sliced thinly; 1/4 teaspoon crushed red pepper; 1/2 teaspoon (scant) black pepper; 1/2 teaspoon (scant) chili powder; 1/2 teaspoon (scant) ground cumin; Flour, for rolling pastry; 1 sheet frozen puff pastry, thawed according to package directions; 1 egg; 1 tablespoon heavy cream; Fresh thyme leaves; Pinch of fleur de sel, for serving