FOR GAJAR HALWA:Heat ghee on medium flame in thick bottomed saucepan.
Add shredded carrots and cook stirring frequently till carrots are softened and shrunk.
Add condensed milk and milk and cook further till the mixture comes together and most of the moisture is lost.
Add sugar and cardamom powder. Stir well till sugar is completely dissolved. Cook for additional couple of minutes.
Switch off gas and let the Halwa cool down thoroughly. --------------------------------
FOR CUPCAKES:Preheat oven at 350 deg F. Place cupcake liners in the muffin pan.
Sift flour, baking powder, and salt together.
In a large bowl, cream together butter and sugar with handheld mixer.
Add eggs one at a time to the creamed butter and whisk till completely merged.
Add vanilla extract to the mixture and give a quick whisk.
Add flour in three parts to wet ingredients and mix it in one direction with wooden or silicone spatula (avoid handheld mixer).
Spoon cake batter less than half in the cupcake liner.
Now add 1 teaspoon of gajar halwa in the center of the batter and then top it off again with cake batter. (Cupcake should be filled about 3/4th of it's entirety).
Place the pan in the center rack and bake for 15-18 minutes or till tooth pick when inserted in the cake comes out clean.
Remove pan from oven and let cool on kitchen counter. Once cooled, serve immediately.