Preheat oven to 350 degrees F and grease a 9x13" pan.
In a large bowl, add cooked rice, tomatoes, Parmesan, soft goat cheese, spices, and salt. Mix until just combined, being gentle so it doesn't turn to mush! Set aside.
In a skillet over med-high heat, add ghee or oil and onion. Saute until onions becomes translucent.
Add garlic and veggies and saute for another 4-5 min.
Add GF flour and stir well for another ~2 min, so that the mixture becomes sticky and the flour no longer looks "raw." It's ok if small lumps form.
Add in milk and stir continuously, breaking up any flour lumps, until the mixture starts to bubble and thicken to the point where it leaves a coating on the spoon.
Pour the liquid mixture from the skillet into the bowl with the rice and other ingredients. Fold in until just combined.
Scoop into the prepared pan and smoothe top with a spatula. Cover with shredded goat cheddar or mozzarella, then bake in oven for 35-40 min.
Turn oven to broil for 4-5 min, or until the top is golden and crispy to your liking (watch closely to prevent burning!).
Let rest for 10 min before cutting.