Heat the oven to 175 C / 350 F with a rack in the center and a sheet pan 33 x 46 cm / 13 x 18 inch on the rack below. Peel, core, and cut the pears into 1 cm / 1/2-inch wedges. Whisk the flour, baking powder, fine salt, and cinnamon together in a bowl.
Melt 60 g butter in a 25 cm / 10-inch oven-safe skillet over medium heat. Stir in the brown sugar and cook for 2 to 3 minutes, stirring, until the mixture bubbles steadily and looks glossy. Stir in the cream, then take the skillet off the heat and sprinkle the flaky salt over the surface.
Arrange the pear wedges in the caramel in tight, overlapping circles, working from the outer edge to the center. Pack them snugly because they shrink as they bake.
Beat 115 g softened butter and the granulated sugar in the second bowl with a hand mixer for 2 to 3 minutes, until pale and fluffy. Beat in the eggs one at a time, then the vanilla. Stir in the flour mixture in three additions, alternating with the buttermilk and starting and ending with flour, until just combined.
Dollop the batter over the pears and spread it to the edge with an offset spatula, nudging gently so the fruit doesn't shift. Bake for 40 to 45 minutes, until the top is deep golden and a toothpick in the center comes out clean.
Set the skillet on a rack and cool for 10 minutes, no longer, so the caramel stays fluid. Run a thin knife around the edge, set a 30 cm / 12-inch plate over the skillet, and flip in one motion while wearing oven mitts. Lift the skillet away, tuck back any stray wedges, and let the cake stand for 5 minutes before slicing.