Trim ends off of the asparagus. Cut the stalks into diagonal, half-inch pieces, leaving the asparagus tips intact. Set aside.
In a wide skillet, melt ghee or oil over medium heat. Add the small asparagus pieces plus a big pinch salt. Cook, stirring until bright green and crisp tender. Remove from pan. Add the asparagus tips and cook for one minute.
In a large bowl, whisk together the flours, salt and pepper. Add two of the eggs and whisk smooth. Add the remaining four eggs, two at a time, whisking well after each addition. Whisk in the milk, cream, and shallots. Set aside.
Spread the small pieces of asparagus in the bottom of the pan. Then add the salmon in pieces. Sprinkle most of the cheese over the asparagus pieces.
Pour the quiche batter over the asparagus and arrange the asparagus tips on top. Sprinkle with the remaining cheese.
Bake the quiche for 30 minutes or until puffed and golden. Let cool for a few minutes, then cut into wedges. Serve warm or at room temperature.