Preheat the oven to 325 and butter a 10" tart pan.
Mix together the walnuts, butter, sage and sugar to form the crust. Press into your prepared tart pan. Bake for 10 minutes or until edge is golden brown. Set aside to cool while you make your filling and turn the oven up to 350.
Melt the butter for the filling in a saucepan, then add the shallots and cook over medium-high heat until caramelized, about 8 minutes. Pour the shallots into the crust.
In a food processor, combine the goat cheese, butternut, salt, pepper, cream and eggs. Once combined, add the rosemary and sage and process just until mixed in.
Pour your cheese and butternut mixture into the prepared tart pan (you may have some leftover, which you can bake by itself in a ramekin). In a bowl, toss your brussel sprouts with the olive oil. Then press the brussel sprout halves into the tart, cut side up.
Bake at 350 for 30-40 minutes, until your brussel sprouts look brown and delicious and the tart, when shaken lightly, remains firm. Allow to cool for 10 minutes to set, then enjoy!