Cheesy Kale and Mushroom Strata

Name: Cheesy Kale and Mushroom Strata
Ingredients: 13 oz. sourdough or country-style bread, cut into 1½ pieces (about 7 cups); 2 Tbsp. extra-virgin olive oil; 8 oz. crimini mushrooms, sliced ¼ thick; 2 garlic cloves, thinly sliced; 1 tsp. kosher salt, plus more; ½ tsp. freshly ground black pepper, plus more; 2 Tbsp. unsalted butter, divided; 3 leeks, white and pale green parts only, halved lengthwise, sliced crosswise ¼ thick; 1 bunch curly kale, ribs and stems removed, leaves torn into 2 pieces; 8 large eggs; 2 Tbsp. whole grain Dijon mustard; 2½ cups whole milk; 5½ oz. Gruyère or Comté cheese, coarsely grated, divided; 2 oz. Parmesan, finely grated, divided