Lightly coat two individual 10 to 12 oz ramekins or one small 5×5 inch casserole dish with non-stick spray. Press the bread firmly into the bottom to cover, patching as needed.
In a medium bowl, whisk the eggs, almond milk, flaxseed, smoked paprika, garlic powder, and black pepper until smooth and slightly frothy.
Pour the custard evenly over the bread.
In a small bowl, toss the ham, bell pepper, and cheddar. Sprinkle evenly over the custard.
Cover tightly and refrigerate for at least 5 hours or overnight.
Preheat the oven to 350°F (175°C). Uncover and discard the plastic wrap. Let rest at room temperature for 15 minutes.
Bake until the center is set and an instant-read thermometer inserted in the center reads 165°F. Bake 20 to 22 minutes for two ramekins, or 25 to 30 minutes for a 5×5 inch dish.
Rest 5 minutes, garnish with chives, and serve.