In a small bowl, warm up milk and 1 teaspoon ghee/butter in the microwave.
Add the warmed milk and ghee mixture to besan and rub with with your fingers till mixed through. Keep aside for a few minutes. Set a fine stainless steel mesh sieve over a deep bowl. Run the prepared besan through the sieve into the bowl. Using a wooden spoon might help. This might take some elbow grease but this extra step is worth it to give pedaas some grainy texture, which might otherwise be ‘pasty’. Take out the seeds from the green cardamom pods and grind them into a powder.
Set a deep, heavy bottomed pan over medium high heat and add ghee or butter into it. Wait till ghee melts. If using butter, let it melt and let it heat up for a minute. If you are a fan of non-stick pans, feel free to use one. Add besan to the pan and lower the heat to medium. Start roasting the besan and stir it continuously to avoid burning. After about 5-6 minutes, the besan will start changing its color to a deeper golden and your kitchen will be filled with a beautiful toasty aroma. Since there is not as much ghee in this recipe as compared to besan burfee, roasting besan while stirring it takes some effort. Keep at it.
At this point, turn the heat off and add sugar and cardamom powder. Mix thoroughly. Let the besan pedaa mixture cool in the pan.
Line a cookie sheet or plate with parchment. Once the mixture is cool enough to handle but still warm, take about a tablespoon of it and form into a smooth ball. Then press it slightly to form a disc. If the edges break, seal them together using your fingers. You can use some warm milk to accomplish this step, if needed. Place the pedaa on the lined cookie sheet. Repeat until the entire besan mixture is used up.
Let the pedaas set in the refrigerator for about one hour. After which, take them out and store in an air tight container. These pedaas store well in the refrigerator. Best served at room temperature. Hah - good luck with keeping them “stored” for too long...Enjoy!