Preheat oven to 350 degrees
Chop the carrots into matchstick size pieces. You can use the food processor but I find something therapeutic about standing up and cutting the carrots into sticks. You have to watch out though; it can become a little obsessive trying to make them all the same size.
Melt a tablespoon of butter in a large fry pan, add the carrots and dill, (the pungent flavor of dill adds a unique blend to the carrots) cook on medium heat until soft about 8 minute’s salt and pepper to taste. Set aside.
In the same pan add the other tablespoon of butter - sauté the onions until soft. Turn the heat up to medium high and toss in the sliced mushrooms. Cook the mushroom fast so that they don’t release too much moisture, let them brown a bit, add salt and pepper to taste. Set aside in a separate bowl from the carrots.
Place the broccoli in boiling water and cook for 3 minutes. Drain; add salt and pepper to taste add butter if you wish I left it out and just added the salt and pepper. Chop the broccoli into small pieces and set aside in a separate bowl from the other vegetables.
To make the sauce place all the ingredients into a container or you can use the food processor. I used a drop down blender. Blend until creamy and smooth.
Fill the bottom of a large muffin tin with some grated cheese, press down. Add a layer of broccoli then some cheese then liberally spoon some of the sauce over the layer.
Add the next layer of mushrooms, cheese and sauce. Press down on each layer.
Now add the carrots and cheese and spoon on the rest of the sauce. The cream should be visible almost to the rim of the pan.
Place the muffin in the oven for 50 minutes or until a toothpick inserted comes out clean and the top is nice and browned.