Heat a pan on low flame and dry roast the aval until crisp. Add the grated coconut and roast along with aval until moisture-free and aromatic. Switch off the flame and allow it to cool completely.
Transfer the cooled aval and coconut mixture to a mixer and grind coarsely to a rava-like texture. Do not grind into a fine powder. Keep this mixture aside.
In the same pan, heat 1 tablespoon ghee and roast the cashews until golden brown. Remove and keep aside.
Add the crushed jaggery to the pan along with 1.5cup of water. Heat gently until the jaggery dissolves completely. Strain the syrup to remove impurities.
Return the strained jaggery syrup to the pan, add the another 2tbsp of ghee, and bring it to a rolling boil on medium flame.
Slowly add the ground aval–coconut mixture to the boiling jaggery syrup while stirring continuously to avoid lumps, adding the ghee little by little as you mix.
Keep stirring the mixture until it thickens and the ghee separates from the mixture and leaves the sides of the pan.
Add cardamom powder and roasted cashews. Mix well and switch off the flame.
Grease a tray with ghee and transfer the mixture. Level the surface evenly. Allow it to cool and set completely before slicing into burfi pieces.