In a small pan, place chestnuts, water and 1/4 cup of sweetened condensed milk.
Cook over medium heat. Once starting to boil reduce heat to low and cook for about 15-20 minutes. Until liquids have reduced and thickened a bit.
Place the chestnut along with the liquids in a bowl of a food processor and pulse until smooth.
Pour the remaining of the sweetened condensed milk in a medium boil over a pan with boiling water (double boiler) and add the chestnut paste and orange zest.
Cook for about 12-15 minutes stirring occasionally. Until the paste has thickened.
Remove from heat and store in a container until ready to use.
In a small pan add butter and cook over medium heat until the butter is brown and has a nutty aroma. Pour into a cup and allow it to cool.
Sift together flour, baking powder, and baking soda.
In a bowl of a standing mixer, add the sugar and orange zest and rub the sugar with your fingers to infuse the zest.
Add the eggs and beat using the whisk attachment medium speed for about 2 minutes.
Stop the mixer and add the coffee, orange juice, and vanilla extract. Gently stir with a rubber spatula.
Gently fold in the flour mix.
Place the batter in the refrigerator for 1 hour.
Butter and sprinkle with flour 12 cavities madeleines pan.
Fill each cavity halfway with batter and scoop 1/2 - 1 tsp of chestnut madeleine. If time permits, place back in the refrigerator for 1 hour.
Preheat oven to 400F and bake for 10 minutes.
Remove from the oven and let cool for 5-10 minutes before removing from pan.
Melt chocolate and vegetable shortening dip Madeleines halfway in.