Not sure exactly what you are making, I've never heard of a "NY special square".

Is it like a chocolate bar, or a hard/solid chocolate topping on something like a cake or bar cookie?
That said, if you are trying to cut through solidified chocolate, you have two options....
The first is to deeply score the chocolate (or cut it) before it has hardened completely.
The second (if the layer of chocolate is thin enough) would be to use a heated knife to cut through it (Dip the knife blade into boiling water, then quickly dry the blade so no water gets on the chocolate). Depending on the size of the area you have to cut through, you will have to keep repeating the procedure as the knife blade cools until all the chocolate is cut.
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If it is a chocolate topped bar cookie like the following, then you must cut it before the chocolate has completely hardened:
NEW YORK SPECIAL COOKIE BARS
1/2 c. butter
3 tbsp. cocoa
1 tsp. vanilla
1 c. shredded coconut
1/4 c. butter
1 tsp. vanilla
2 sq. bitter or semi-sweet chocolate
1/4 c. sugar
1 egg
2 c. crushed graham crackers
1 c. chopped walnuts
2 c. powdered sugar
Milk
1 tbsp. butter
In double boiler or microwave stir together 1/2 cup butter, 1/4 cup sugar and cocoa until smooth. Add 1 beaten egg and 1 teaspoon vanilla and cook until thickened. Remove from heat and add graham crackers, coconut and walnuts. Press firmly into 8x8 pan. Chill.
Mix 1/4 cup butter, powdered sugar, 1 teaspoon vanilla and enough milk to spread. Spread over other mixture and chill.
Melt chocolate with 1 tablespoon butter.
Drizzle or spread over other chilled mix. Cut into small squares.
Freezes great! Best kept refrigerated. Double recipe and use a 9x13 pan.
Note: I find using a metal bench scraper/dough cutter to be the best thing for slicing brownies or bar cookies because you just push it straight down through whatever you have to cut, instead of using a sawing motion like you have to do with a knife.
