In a bowl, whisk together the flour, sugar, baking powder, and salt. Drop in the cubes of butter, and either with your hands, a fork, or a pastry cutter, smush the butter into the flour.
Scoop in the creme fraich and gently work the flour into it until a shaggy ball forms. Add only as much water as you need to get it to come together. Some shaggy dough is still fine.
Place dough in the center of a sheet of plastic wrap and twist it sealed. Chill for 2 hours or overnight.
When ready, divide the dough in half. Roll one half into a flat round and drape over an ungreased tart pan. Press dough into the grooves of the pan and trim the excess.
Spread the carrot pudding filling evenly into the tart.
Roll the second half flat and cut into thin strips with either a knife or pastry cutter. Carefully create a lattice pattern with the strips. You can also create a braid out of the strips to drape around the circumference of the tart pan.
Brush with a beaten egg.
Bake at 425°F for 20 minutes on the middle rack, then lower the heat to 400°F for another 10 minutes, and 375° for a final 10 minutes. Check on it frequently to ensure the crust does not burn. Cool completely before cutting.
With the remaining creme fraiche, add vanilla bean paste or extract and sugar to desired taste. Take a spoonful and drop it on a serving plate. With the spoon facing up, place the bottom of the spoon on the dollop and swipe the creme fraiche along the plate for a little flair. Serve next to a slice of tart.