Preheat the oven to 400°F. Place the bread cubes in a large bowl and pour 2 tablespoons of the olive oil over top. Toss to coat. Place the bread cubes on a large baking tray and transfer to the oven. Bake for 10-15 minutes or until golden brown.
Crumble the goat cheese into a large bowl. Slowly whisk the milk into the goat cheese until smooth and well integrated. Crack the eggs into the milk mixture. Add the lemon juice, Dijon mustard, 1 teaspoon of the salt, cayenne, and chives. Whisk to combine. Set aside.
Heat the remaining olive oil over medium heat in a large skillet until shimmering. Add the onion and the remaining salt. Saute until just translucent. Add the garlic and saute until fragrant, about 2 minutes. Add half of the spinach and saute until wilted. Add the remaining spinach and repeat. Remove from the heat and let cool slightly.
Butter a 7x9 baking dish, set aside. Place the toasted bread, artichoke hearts, and the sauteed spinach in a large bowl. Toss to combine. Transfer the bread to the baking sheet and press into an even layer. Pour the egg mixture over top. Wrap the baking dish in plastic wrap and place in the fridge. Let chill overnight.
Preheat the oven to 350°F. Dot the surface of the strata with the butter. Sprinkle the top with the shredded asiago and transfer to the oven. Bake for 50 minutes or until golden brown. Let cool for 10 minutes before serving.