How to Make It
Heat 1 1/2 teaspoons oil in a Dutch oven over medium-high. Add artichokes and 2 garlic cloves; sauté until fragrant and softened, about 4 minutes. Remove from pan. Add remaining 1 tablespoon oil and 2 garlic cloves; cook, stirring often, 30 seconds. Add spinach gradually, tossing constantly until spinach wilts, about 3 minutes. Transfer spinach to a strainer to cool.
Whisk together milk, salt, pepper, and eggs in a large bowl. Squeeze spinach to remove excess moisture. Add spinach, artichokes, bread, and garlic-and-herb cheese to milk mixture; toss well to combine. Spoon bread mixture into a 13- x 9-inch glass or ceramic baking dish coated with cooking spray; sprinkle with Swiss cheese. Cover, and chill 8 hours or overnight.
Preheat oven to 350°F. Let the strata stand at room temperature while the oven preheats.
Uncover strata, and bake at 350°F until set and lightly browned around the edges, about 45 minutes. Remove from oven; let stand 5 to 10 minutes before serving.