Using an electric mixer, cream the brown sugar and unsalted butter together until fluffy. Add the remaining cookie ingredients and beat until well combined. Wrap the dough in plastic and refrigerate for at least one hour.
Preheat the oven to 350 degree F and line several cookie sheets with parchment paper. On a floured work surface, roll out the dough until it's 1/8-inch thick. Use a round 2 1/2-3 inch cookie cutter to cut out the cookies. Place them on the prepared cookie sheets, 1 1/2 inches apart. Gently insert a lollipop stick into each unbaked cookie before baking.
Bake for 13-16 minutes until golden around the edges, yet soft in the center. Remove from the oven and cool completely on the cookie sheets.
Melt the butter and chocolate together. Either do this over a double-boiler on low heat, or place in a microwave-safe bowl and nuke in 30-second increments, stirring in between, until it's just barely melted. Continue to stir until all the chunks melt away.
Cut the Peeps apart. If you have it, dip the exposed portion of the Peeps in colored decorating sugar.
Spread the melted chocolate on top of each cookie. Place a lollipop stick on each cookie and turn in the chocolate to coat the tip. Gently press a Peeps over the top of the stick. Sprinkle the chocolate with Easter sprinkles. Set aside until the chocolate hardens. (If you're in a hurry, place the cookie sheets in the fridge for 5 minutes to harden the chocolate.)
