Bring a large pot of salted water to a rapid boil over high heat. Add the baby spinach, then cook until the spinach has wilted. Drain over a colander, then squeeze out as much excess water as possible. Set aside.
Melt butter in a large skillet over medium heat. Add 1 chopped shallot then season lightly with Kosher salt. Cook, stirring occasionally, until translucent. Add chopped garlic, then cook.
Add flour, then use a whisk to stir until the flour is completely absorbed. Slowly pour in milk and heavy cream. Add grated nutmeg, then stir well. Bring the mixture to a boil, then reduce the heat and simmer. Meanwhile, preheat a broiler to high with an oven rack about 6-inches below the heating unit.
To the skillet, add the blanched spinach. Cook, stirring occasionally then sprinkle on about ⅔ of both the Gruyere and Parmesan cheeses. Stir well, then transfer to the prepared baking dish. Sprinkle the remaining Gruyere and Parmesan on top. Serve immediately!