Cut baguettes into approximate 1" cubes and set aside. Dice onion and cut up asparagus and set aside, as well.
Heat olive oil in a skillet set over medium heat. Add onion and asparagus to the skillet and stir frequently while cooking for 6-7 minutes, or until the asparagus has softened slightly and the onions have become a bit golden. Transfer to a large bowl to cool slightly.
Place sausage to the skillet set over medium heat and break up into crumbles. Continue to crumble and stir the sausage as it cooks, until it's no longer pink. Once fully browned, transfer sausage crumbles drained of the fat to bowl with the onion and asparagus.
Add parsley, salt, pepper, and Asiago cheese to the bowl and stir to combine everything.
In a separate bowl, whisk together eggs, chicken broth, and milk. Pour the liquid mixture into the bowl with the other ingredients and stir so that the liquid evenly coats everything.
Cover bowl with plastic wrap and refrigerate for at least 4-5 hours, or overnight.
When ready to bake, preheat oven to 350°F. Spray a 10"x14" baking pan* with cooking spray and evenly spread the strata ingredients in the pan. Press down slightly to pack it all in.
Cover pan with aluminum foil and bake for 30 minutes. Take off the foil and bake for another 45 minutes, or until the top baguette pieces are golden brown and the strata is pretty much set and a tester inserted in the middle comes out clean. Let strata rest for about 10 minutes before slicing and serving.
*It's optimal to use a 10"x14" baking dish or a 4 quart casserole dish for this strata. In a pinch I've also used a 9"x13" baking dish, though it was filled to the brim. A 9"x13" dish will work, however I suggest putting a large baking sheet on a rack underneath the strata to catch any splatters or drip overs before they hit the oven floor.You'll want to use a big bowl to combine all the strata ingredients so the baguette pieces don't fly out when you mix everything up!Prep time doesn't include the time necessary for the strata ingredients to refrigerate. This can be anywhere from four hours to overnight - it's flexible.