Spray the insides of 2 4.25" diameter, 14 ounce ramekins with olive oil cooking spray and set aside.
Cook the cauliflower, in the microwave or steamer until soft, 3-5 minutes. Pour the cooked cauliflower into a sieve and let drain and cool completely.
While the cauliflower is cooling, slice, dice and prepare the vegetables. Spray a non-stick skillet with olive oil spray and add the carrots, onion, potato, and celery. Cook over medium heat for 7-8 minutes, stirring frequently until the vegetables are just fork tender, not mushy! Set aside.
Preheat the oven to 425 degrees.
In a medium bowl add the Parmesan, flour, salt, and pepper.
When the cauliflower is completely cool place it on folded paper towels. Place more folded paper towels over the top and press down with your hands until all the water is expressed.
Stir the caulifower into the flour mixture, then add the beaten egg. Mix well. Remove and set aside ½ of the crust mixture for the tops. Divide the rest into two portions and press into the bottoms of the ramekins with wet fingers.
Place the ramekins on a baking sheet. Bake for 10-12 minutes or until the crusts are set and a bit brown on the edges. Remove from oven and set aside.
In a small bowl add the milk, chicken broth, flour, thyme, garlic, and salt. Stir. Pour into the skillet with the vegetables and heat until the sauce is just bubbly and just begins to thicken. Remove from heat and add the diced chicken. Stir just to mix.
Divide the filling mixture amongst the ramekins with bottom crusts.
Divide the reserved crust mixture into two portions. Cut parchment paper into circles the size of the ramekins. Using wet fingers, press the crust onto the parchment paper and shape it into circles the diameter of the ramekins. Flip the parchment over in your hand and gently peel the paper off. Place the discs of crust on top of the filling. (see photos)
Reduce the oven to 400 degrees and bake until the filling is heated through and bubbly and the crusts are golden brown. Brush with olive oil, sprinkle with the Parmesan cheese, a bit of thyme, and cracked black pepper. Cool just slightly before serving,