Fill a large bowl with ice and cold water and set aside. In a large pot bring the water and 1 tablespoons salt to a boil over high. Add the spinach and cook, stirring constantly, until the spinach has wilted, about 1 minute. Using a slotted spoon. a spider or tongs, transfer spinach to prepared ice water to stop the cooking process. Allow to  cool for about 1 minute. Drain well in a colander and then place spinach on a clean kitchen towel and squeeze firmly over sink to remove as much liquid as possible. Put spinach in a food processor and pulse until roughly chopped, about 5 or 6 pulses. Set aside.

Preheat the oven to 350°F with rack in the middle. Meanwhile, melt 2 1/2 tablespoons of the butter in a 10-inch cast-iron skillet over medium-high heat. When the butter has melted and stops bubbling, add the onion and cook, stirring occasionally, until tender, about 4 minutes. Add the garlic and cook, continuing to stir constantly, until fragrant, about 30 seconds. Reduce the heat to medium. Whisk in the flour, mustard, cayenne, nutmeg, and remaining salt. Cook, stirring constantly for about 1 minute. Gradually whisk in milk until combined. Bring the mixture to a boil over medium heat, whisking occasionally. Boil, continuing to whisk occasionally, until a thick sauce forms, about 2 minutes. Stir in cheddar and about 2/3s of the Pepper Jack cheese. Continue to cook, stirring constantly, until smooth, about 1 minute longer. Remove the skillet from heat and stir in the reserved spinach until well combined. Sprinkle evenly with remaining Pepper Jack cheese and dot with small pieces of the remaining butter.

Bake in the preheated oven until bubbly, about 15 minutes. Leave the skillet in place and increase the oven temperature to broil. Broil until browned in spots, about 2 to 5 minutes. Let stand at room temperature for about 5 minutes before serving.