Position a rack in the upper third of the oven and preheat to 350ºButter a 10" oven-proof skillet with the 2 teaspoons of softened butter.
In a small bowl, stir together the sugar, cardamom, ginger, and cinnamon. Set aside 2 tablespoons to top the cake; add the rest to the butter. Cream together the butter and spiced sugar in the bowl of a stand mixer on medium speed until light and fluffy, scraping down the sides of the bowl once or twice, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
In a medium bowl, sift together the rice, millet, oat, and buckwheat flours, baking powder, and salt. Add half of this mixture to the butter, stir on low until just combined. Add the crème fraîche and vanilla, stir on low until just combined, then add the remaining flour mixture, stirring on low until just combined.
Remove the bowl from the mixer, and give it a gentle stir with a rubber spatula, scraping the bottom and sides to make sure the batter is homogenous. It will be thick and spongy from the baking powder reacting with the acids in the crème fraîche.
Cut the pears off of their cores. Cut some of the pear pieces into enough 1/2" cubes to equal 1 cup, and slice the rest into 1/2" thick (at the widest parwedges. Drizzle the lemon juice over the wedges; this keeps them from oxidizing, and gives them a little punch. Gently fold the pear chunks into the batter, then spread the batter evenly into the greased skillet.
Fan out the pear slices over the top of the cake with the fatter part facing out. Press them into the batter a little bit; I like to place them at a diagonal so that some cake batter peaks through the fruit. Sprinkle the reserved 2 tablespoons of spiced sugar evenly over the top.
Bake the cake until the top is golden and set, the sides are pulling away from the pan, and a toothpick inserted in the center comes out clean, 45-55 minutes. Since the cake is still cooking from residual heat, let it cool for at least an hour before cutting it into wedges and devouring it with your afternoon (or, ahem, breakfast) tea.
Leftovers keep well at room temperature for a day or two; refrigerate the rest after that.