Make the mornay sauce: In a small saucepot over medium heat, melt butter and add shallots, garlic, bay leaf, and thyme. Cook for 2 minutes, then discard bay leaf and thyme. Add flour and stir constantly for 3 minutes. Add milk, increase heat to medium-high, and stir frequently until milk starts to thicken. Stir in wine, reduce heat to low, and stir for 3 to 4 minutes. Season with salt, pepper, and nutmeg. Remove from heat, stir in cheddar cheese, and keep warm on stovetop until ready to use.
Make the cauliflower gratin: Preheat oven to 375 degrees. Bring a large pot of salted water to a boil over high heat. Cut cauliflower into medium to large florets. Boil florets for 4 minutes, then drain. In a medium casserole dish, add a third of mornay sauce to coat bottom; top with cauliflower. Pour remainder of sauce over cauliflower and stir to coat. Sprinkle with breadcrumbs and cheese, then bake until golden brown and bubbling, about 30 minutes.