In a medium saucepan over medium heat, combine the potatoes, butter, honey, salt and 2/3 cup of water. Bring to a boil, stirring to melt the butter then reduce to low heat, cover and cook for 15-20 minutes. The potatoes are finished cooking when a skewer or paring knife meets no resistance.
Transfer the potatoes and any liquid to the bowl of a stand mixer. Cool until just warm, around 30 minutes. Mist a medium sized bowl with cooking spray.
Using the paddle attachement, beat the mixture on low until smooth, 1 minute. Switch to the dough hook and add the flour and yeast. Mix on low until a smooth dough forms, 5 minutes. Increase to medium-high and knead for 1 minute to help strengthen the dough. Transfer to the prepared greased bowl, cover with plastic wrap and let rise in a warm space (like an oven with the light on) until the dough has doubled in size, approximately an hour.
Heat the oven to 350 F with a rack in the middle position. Line a rimmed baking sheet with parchment paper.
Turn the dough out onto a lightly floured surface and divide into 8 pieces. Form each piece into a tight ball by rolling in a circular motion on the counter. Place seam down on the baking sheet. Using your hand, press and flatten each ball until it measures 4 inches wide and 1/4 inch thick. Cover with plastic wrap and let rise until doubled in size, about 30 minutes.
Heat a nonstick skillet over medium heat. Place 4 dough rounds seam-side down in the pan and cook until golden brown, as you would homemade English Muffins. Using a wide metal spatula, flip and cook the second sides until golden brown, around 1 minute. Repeat with the remaining rounds, returning them to the baking sheet.
Bake the flatbreads in the oven for 12-13 minutes. Immediately transfer to a wire rack and let cool for 15 minutes. Serve with garlic chive butter.