Preheat your oven to 400°F. This ensures that your tart will bake evenly and achieve that lovely golden color. While waiting for the oven, prepare your baking sheet by placing parchment paper on it. This will prevent the phyllo pastry from sticking.
Next, fill a 9 x 13 baking dish with ice and water, and keep it in the freezer until you're ready to use it. This ice bath will be essential for stopping the cooking process of the asparagus later on.
In a large skillet, bring about an inch of water to a boil. Once boiling, add the asparagus and cook for about 2 to 5 minutes until they turn bright green and tender. Keep an eye on them; you want them to retain some crunch.
Once cooked, carefully drain the hot water and immediately plunge the asparagus into the ice bath. This helps to lock in the vibrant green color and stop the cooking process. After a few minutes, transfer the asparagus to a bed of paper towels or a clean kitchen towel to dry, pat gently to get rid of excess moisture.
In a small saucepan over medium heat, melt the butter. Stir until it bubbles and the color turns a pale amber, which indicates it's ready for the shallots. Add the diced shallots and stir for about a minute while being careful not to burn the butter.
Once the shallots are tender, remove the saucepan from heat and let the mixture cool slightly. This flavorful butter will later drench the asparagus, enhancing its natural taste.
Roll out the thawed phyllo sheets carefully. Brush each sheet with the melted butter and layer them on top of each other (around 8 to 10 sheets) in your prepared baking sheet. This will create a beautiful, flaky crust. Bake the layered phyllo for about 10 minutes or until golden brown.
Once the phyllo is baked, return the cooked asparagus to the dry skillet and pour the remaining butter and shallot mixture over it, coating each piece thoroughly.
Now, sprinkle a generous amount of Fontina cheese over the baked phyllo sheets. Next, place the asparagus side by side over the cheese, creating a beautiful arrangement.
Finally, season the tart with kosher salt and pepper to taste. Bake for another 10 minutes or until the cheese has melted and is bubbling, creating a delightful aroma throughout your kitchen.