Cook the potatoes in a pan of boiling, salted water for about 20 minutes, or until soft. Drain and allow to cool. When cool enough to handle, peel off the skins.
Heat enough oil for shallow-frying in a kadhai or wok over medium-high heat.
Add the potatoes and shallow-fry for about 10 minutes, or until golden brown. Remove and drain on kitchen paper (paper towels).
Put the cottage cheese in a bowl, add the yoghurt, and stir to combine.
Cut a thin slice off the top of each potato and set it aside.
Using a sharp knife, make a hollow in the potatoes, making sure the skin is not punctured, and scoop out the potato flesh into a bowl with a teaspoon. Set the hollows aside.
Season the scooped out potatoes with salt, then add the carrots, chaat masala, chopped chillies, coriander and lime juice.
Mix well, then add the yoghurt and cottage cheese mixture and stir until combined.
Stuff the potato hollows with the filling, put the reserved potato slice on top, and sprinkle over some chaat masala before serving.