First of all, grate the butter (using the larger side) into a bowl. Chill the grated butter very well.
Then add the flour and salt to the butter. Rub the butter into the flour, using a tablespoon, by pressing down on the butter-flour mixture with spoon and dragging it against the bottom of the bowl in a sweeping motion. You can work by moving the spoon away from you towards the side of the bowl further from you. This tends to flatten out the grated butter pieces while incorporating it into the flour.
This will result in the butter-flour mixture looking somewhat like crumbs, but with larger and flatter bits of butter in it. Using the spoon also ensures that the mixture remains cold, which is very important to produce a flaky and crisp pie/ tart crust.
Chill this mixture for about 15 minutes. Add the water, a little bit at a time, and knead the dough just enough to bring it together. Do not handle the dough more than necessary. If making a mini-galettes, divide into three equal portions and shape each into a disc. Wrap in cling film and refrigerate for about an hour.
Prepare the filling, in the meanwhile, by cooking the mango pieces, sugar and salt till the sugar dissolves and the fruit is just soft. This should take about 5 minutes. Add the cardamom, cinnamon and clove powders and mix well. Take off the heat.
Take out the dough and lightly roll out each portion into a 1/4″ thick circle. Put 1/3rd the filling in the centre of each circle and sprinkle some brown sugar over it. Gather up the edge of the circle together inwards, covering the filling partially and seal in a pleated fashion leaving the centre of the galette open.
Place on a baking sheet and bake at 190C (375F) for 45 minutes to an hour till the crust is crisp and a golden brown. Cool on a rack and serve warm as it is or with ice-cream or a custard sauce.