Preheat the oven to 325˚F. Butter four 5 1/2" tart molds.
Combine the flours, coconut, baking powder, and salt and thoroughly mix.
Cream together the butter and sugar, mixing on medium-high for about 3 minutes. Add the egg and beat another 2 minutes.
Add the flour mixture, alternating with the cream, in thirds to the bowl. It will be very thick. Spoon the dough into the tart molds. Sprinkle with turbinado sugar.
Bake at 325˚F for 15 minutes, or until a knife inserted in the middle comes out clean.
Melt the butter and mix with the honey. Baste the pineapple slices with the honey-butter and grill on high heat, 2 minutes per side.
Whip the whipping cream using a mixer until soft peaks form. Add the sugar and lime and continue to whip on high for 30 seconds, I like mine with medium stiff peaks - just be careful not to over whip!
Slice each coconut shortcake in half to form a 2-layer shortcake. Place the grilled pineapple in the middle and top with whipped cream.