1. In a medium sauté pan, add butter and heat over medium heat. Add leeks and cook until slightly softened. Add garlic and cook for an additional 2 minutes. Allow to cool slightly.
2. Butter a 9x13 baking dish and alternatively overlap slices of bread and ham until bottom of dish is completely covered.
3. In a medium bowl, add eggs, milk, Dijon, smoked paprika, green onions and reserved leeks. Season with salt and pepper and whisk until combined.
4. Pour liquid mixture over bread and ham and top with grated Gruyere.
5. Cover tightly and refrigerate for 1 hour or overnight.
6. Preheat oven to 375°F. Bake strata, until browned and warmed through, approximately 30 minutes.