On a lightly floured surface, roll out both pizza crusts so you have two 14-inch circles. Place on parchment-lined baking sheets or pizza pans.
Top each crust with half the crushed croutons, leaving a 3-inch border around the edges.
Mix the goat cheese and parmesan cheese together. Sprinkle 3/4 cup over the croutons on each crust. Set aside remaining 1/2 cup of cheese for later.
In a large skillet, melt butter over medium heat. Add drained Dei Fratelli Stewed Tomatoes, mushrooms and thyme. Cook until mushrooms are softened and most of the liquid has evaporated from the pan, about 10 minutes.
Remove from heat and let cool for 5 minutes. Spoon 1/2 the mixture evenly over each crostata.
Take remaining cheese mixture and sprinkle 1/4 cup over tomatoes and mushrooms on each crostata.
Fold crust borders up and over the filling, leaving the center bare, and pleating the crust to make it lay snugly over the filling.
Brush the folded-up crusts of each with the beaten egg. Bake crostatas for 30 minutes, or until the crusts are golden. Let rest for 5 minutes before serving.
To enhance the flavor, sprinkle crust with coarse sea salt after baking.