Heat the oven to 300°F. Line your slow cooker with foil to cover the hot spot and make it easy to remove the finished casserole, then grease the foil with cooking spray. With a vegetable peeler, gently peel the yellow zest from the lemon. Place on a small piece of cheesecloth, then use twine to create a small bag. Place the bag in a small to medium saucepan. Pour in the milk. Bring to a bare simmer over medium heat, then immediately remove the pan from the heat (you don’t want to reduce the milk at all). Cover and let sit for 25 minutes. Set aside.
Place the bread cubes on a baking sheet and bake, shaking a few times, until dry, about 40 minutes. Set aside.
Line a large baking sheet with a kitchen towel. Add 2 Tbs. of oil to a large, heavy nonstick sauté pan and heat over medium-high heat. When warm, add the garlic. Sauté until soft and aromatic but not brown, about 2 minutes. Transfer 2 Tbs. to a large bowl and set aside. Immediately add another Tbs. of oil, one-third of the spinach, plus 1⁄4 tsp. salt to the pan. Using tongs, toss and cook until wilted, about 2 minutes. Transfer to the lined baking sheet. Repeat two more times with the oil, spinach, and salt. Place another towel on top of the spinach. After the spinach cools down a bit, gather up the towels and vigorously squeeze out all of the water (you’ll probably need to do this several times). Set aside.
Add the bread cubes to the large bowl with the garlic and stir well with tongs. In a medium bowl, stir the cheeses together. Pour half of the bread-garlic mixture into the slow cooker, spacing it evenly. Then add half of the spinach, then a bit less than half of the cheese, spacing evenly. Repeat again with the three layers, reserving about 1/2 cup of cheese.
Discard the cheesecloth bag from the milk. In a large bowl, whisk the eggs. Pour in the lemony milk and the mustard, and stir in 1 tsp. salt, the nutmeg, and pepper. Pour on top of the solids in the slow cooker, pressing down firmly with a spoon to submerge them in the liquid. Top with the remaining cheese.
Cover and cook on low until the internal temperature reaches 170°F, about 4 hours (no longer, or the strata can become rubbery or burn). Turn off the slow cooker, remove the lid, and let sit for 30 minutes. Carefully grab the foil handles to lift the strata out of the slow cooker, and place it on a cutting board. Gently peel away the foil, slice, and serve, garnished with fresh chives.