In a bowl of a stand mixer, add brown sugar and butter and beat together until smooth, about 2 minutes. Add flour, salt, and food coloring gel and mix until the food coloring gel is blended well.
Using your hands, remove from bowl and form into a ball of dough. Place on a piece of parchment and the cover with another sheet of parchment. Using a rolling pin, roll into a rectangle about 12x14 inches and ⅛ inch thin. Freeze for 5 minutes.
Remove from freezer. Remove top sheet of parchment paper and place on a baking sheet. Using a round cutter, cut out 24 rounds out of the dough. Place rounds on prepared baking sheet. If needed, roll out the scraps and cut out the needed remaining rounds. Chill until needed.
To make the puffs and assemble:
Preheat oven to 400 degrees. Line two baking sheets with parchment paper or baking mats. Set aside.
In a medium saucepan, heat butter, sugar, salt, and water together over medium-high heat until it boils. Immediately add all of the flour and stir with a wooden spoon. Continue to stir over heat until a firm forms on the bottom of the pan. Remove from heat and transfer dough to a medium bowl to cool down for 3 minutes.
Once slightly cooled, add 1 egg to dough and stir vigorously until combined into dough. Repeat with rest of eggs, one at a time.
Transfer mixture to a large pastry bag fitted with a large piping tip. Pipe 1 1/2 inch rounds onto prepared baking sheets (about the size of a macaron). Make sure to space out about 2 inches apart. Top each dollop of dough with a round of craquelin dough, setting it in the center.
Bake in preheated oven for 15 minutes and then rotate to bake for another 15 minutes. The dough should be puffed and the craquelin will have melted and cracked over the top. Remove from oven. Using a sharp knife cut a small slit in the top or sides of the profiteroles to allow the steam to escape. Let them cool completely.
To make the raspberry whipped cream:
Blend raspberries and 2 tablespoons using a blender. Set aside. Add cold whipping cream to bowl of a stand mixer, along with remaining 4 tablespoons of sugar and 2 teaspoons of vanilla. Blend on medium-high until the cream is super stiff.
Add raspberry puree to whipped cream and gently fold together but not all the way (you want it to be swirled, not combined). Spoon whipped cream into large pastry bag with a star tip.
Cut each profiterole in half. Pipe the whipped cream onto the inside of the bottom half of the cut profiterole. Top with the top half of the profiterole. Repeat with the rest of the profiteroles and whipped cream. Dust with powdered sugar, if desired. Serve immediately or within 12 hours.