From what I know about Italian cookies, you seem to be describing a combination of characteristics from two different cookies. Meatball cookies are a very spicy cookie with a sugar glaze, but Neopolitan cookies are three pastel colors with a light, fruity almond flavor, and usually, a chocolate glaze. So, here are recipes for the two cookies, and you can decide which it is you need.

NEOPOLITAN COOKIES

1 (8 oz.) can almond paste (1 c.), cut into chunks
1 c. butter
1 c. sugar
4 egg yolks
2 c. all-purpose flour
4 egg whites
Red and green food coloring (number of drops desired)
1/4 c. seedless red raspberry jam
1/4 c. apricot preserves
6 oz. semi-sweet chocolate pieces

Preheat oven to 350 degrees. Grease bottom of three 9x13x2 inch pans. Line with wax paper and grease again.
Cream almond paste, butter, sugar, and egg yolks. Blend in flour. Beat egg whites until soft peaks form when beater is slowly raised. Fold egg whites into batter mixture. Divide batter into 3 equal parts (1 1/2 cups each part). Add red food color to first part, green to second, and leave third part uncolored. Spread each part into prepared pans.

Bake 10 to 12 minutes, just until edges are golden brown (watch carefully!). Invert onto wire rack and remove pans. Using another wire rack, turn right side up and cool.
Spread raspberry jam on green layer and top with yellow layer. Spread apricot preserves on yellow layer and top with pink layer. Cover with plastic wrap and lay heavy weighted pan on top. Refrigerate overnight.
Next day, melt chocolate in a double boiler over hot (not boiling) water. Spread on cookie layers. Trim edges. Cut into strips and then cut again diagonally for diamond-shaped cookies. Cookies are best when frosted with the melted chocolate not more than a day before serving.

ITALIAN MEATBALL COOKIES

1 c. shortening, melted
8 c. flour
2 c. sugar
1 c. cocoa
3/4 tsp. cloves
2 c. milk
3/4 tsp. soda
3/4 tsp. cinnamon
1/2 tbsp. pepper
1/2 tbsp. nutmeg
1/2 tbsp. salt
Chopped nuts (optional)
Chocolate chips (optional)

Mix with hands until well blended. Add nuts and chocolate chips if desired. Should be hamburger consistency. If too dry, add up to 1/2 cup milk. Bake at 350 degrees for 15 minutes. Cool. Dip in milk and roll in confectioners' sugar.