Place a steamer basket over a large pot of boiling water. Add green beans and steam for 8 minutes or until just tender and bright green. Alternately you can blanch the green beans in boiling water for 3-4 minutes until just tender. Transfer cooked beans to a bowl of ice water to stop the cooking.
Add 2 Tbl. butter, 1 Tbl. olive oil and 2 sprigs fresh thyme to a large skillet over medium-high heat. Add half of the sliced mushrooms in a single layer and brown on one side without turning, about 4-5 minutes. Turn over mushrooms and brown on the other side, about 3 minutes. Remove from pan and reserve. Melt remaining 2 Tbl. butter, 1 Tbl. olive oil and thyme sprigs. Add remaining mushrooms and brown on both sides. Remove from pan and reserve.
For the Parmesan Cream Sauce
In a medium sauce pan, melt 2 Tablespoons of butter over medium heat until hot and bubbly. Add flour and whisk to combine. Continue cooking until lightly golden brown, stirring constantly. Gradually whisk in half & half. Bring to a gentle boil and cook for 5 minutes, stirring occasionally. Remove from heat and add minced garlic and grated parmesan cheese. Whisk until cheese is melted. Season with salt & pepper to taste.
For the Crispy Shallots
In a medium sauce pan bring 2 cups of vegetable oil over medium-high heat to 375° F. Working in batches, fry sliced shallots until deep golden brown. Remove with a mesh strainer and transfer to a paper towel lined plate. Continue with remaining shallots.
To Assemble Casserole
Preheat oven to 350° F. Arrange green beans in a 3 quart casserole dish. Top with browned mushrooms and parmesan cream sauce. Cover with aluminum foil. Bake covered 35 minutes. Remove foil and bake an additional 15-20 minutes until sauce is bubbling and lightly browned around edges. Add Crispy Shallots and bake an additional 5 minutes. Garnish with shaved parmesan cheese and lemon zest.