Preheat your oven to 400°F (200°C).
Prepare the cauliflower crust by pulsing 1 cup of raw cauliflower in a food processor until it resembles rice. Transfer to a bowl, add the egg white and grated parmesan, then season lightly with salt, pepper, and a pinch of thyme. Mix until combined.
Press the cauliflower mixture evenly into the bottom of a small ovenproof dish to form the crust. Bake in the preheated oven for about 10 minutes until slightly firm.
While the crust is baking, dice the chicken breast into bite-sized pieces. Chop the carrot (using half a medium carrot), celery, and if needed, roughly chop the green peas (if they are whole).
Heat 1 tsp olive oil in a skillet over medium heat. Add the chicken pieces and sauté until lightly browned on all sides.
Add the chopped carrots, celery, and green peas to the skillet. Sauté for an additional 3-4 minutes until the veggies start to soften.
Pour in the chicken broth, low-fat milk, and add 2 tbsp nonfat Greek yogurt. Stir to create a light, creamy sauce. Season with salt, pepper, and additional thyme to taste.
Allow the filling to simmer for 3-4 minutes until the flavors meld and the sauce slightly thickens.
Remove the crust from the oven and gently spoon the creamy chicken and vegetable mixture on top of the pre-baked cauliflower crust.
Return the dish to the oven for an additional 10-12 minutes to heat through and allow the flavors to meld together.
Remove from the oven, let cool slightly, and serve warm.