Preheat the oven to 375F (180C) and arrange a rack in the center.
In a 10" (25cm) oven proof skillet, I use a cast iron skillet, heat the oil until it shimmers. Add the mushrooms and sear them, stirring only a few times, for 7-8 minutes on medium high heat. They will release their juices and turn a dark color.
Turn the heat to medium low and add the shallots. Saute' for about 3 minutes or until the shallots just soften. Stir in the garlic, 3/4 tsp sea salt, pepper and rosemary. Then, sprinkle in the flour/tapioca. Stir to coat the veggies, one minute. Pour in the broth and bring simmer for about two minutes or until the mixture starts to thicken, stirring occasionally. Pour in the milk, stir, and bring to a simmer.
Reduce the heat and cook on medium low for about 7-8 minutes, until the sauce thickens a bit. It will be a thinish gravy, but will thicken further in the oven. Taste for seasoning adjustment. Stir in the beans and coat with the creamy mushroom mixture.
At this point the casserole can be covered and stored in the refrigerator for up to 24 hours.
Just before baking, sprinkle the bread crumbs evenly over the top of the casserole. Bake at 375F for 25-30 minutes or until bread crumbs are toasty/crisp and the casserole is bubbly.
Store leftovers in a lidded container in the refrigerator for up to three days. Reheat in a 350F oven for about 10 minutes.