Mix warm water, yeast and sugar together in a small bowl. Set aside until foamy.
Add buttermilk, mashed potatoes, eggs, salt, sugar, and butter, whisk well. Add flour and mix in until a soft dough forms and the butter thoroughly incorporated.
Knead the dough by hand for 8 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with plastic wrap, and let rise and room temperature until doubled in size, 1 – 1 ½ hours. Deflate the dough, recover the bowl, and refrigerate overnight, or for at least 5-6 hours until well chilled.
Before shaping danish, make fillings.
Cherry Red Raspberry Filling: combine all of the ingredients in a small saucepan and bring to a boil over medium heat while stirring constantly. Reduce heat and simmer for 5 minutes, then remove from heat and cool.
Cream Cheese Filling: combine all the ingredients in a bowl and mix until combined
Egg Wash: combine the egg and milk in a bowl and beat until combined.
Icing: combine all ingredients until a smooth icing forms. Set aside until Danish are baked and cooled for 15 minutes.