In a stand mixer bowl, cut the flour and butter together until no pieces of butter can be seen.
In a bowl or jug, mix together the water, yeast, salt, and sugar, and mix to combine. Then add this to the flour and the starter, continue to mix until a ball of dough is formed.Knead the dough in the bowl for 5mins, until smooth and stretchy. Then place the dough in a greased bowl, cover, and rest until doubled in size - about an hour. Lay a sheet of baking parchment paper on a large baking sheet, and scatter cornmeal/polenta loosely over the top.Roll the dough out on a lightly floured surface, and press it out until 1.5cm/½-inch thick. Then, using a scone/biscuit cutter, about 3½-inch/8cm round, cut the muffins.Place the cut discs on the cornmeal/polenta tray, and cover with a tea towel before allowing to rest/prove for 20-30mins.
Heat your oven to 200˚C/400˚F.
Over med-high heat, warm a greased griddle or heavy-based pan until hot. Cook the muffins for 2mins on each side - don't crowd the muffins, do them in small batches.
Bake the muffins for approx. 10mins, or until lightly browned.
Remove from the oven, and rest for at least 30 minutes before eating.
To open a muffin, use a fork and pierce your way around the edge of the muffin. Push the prongs of the fork all the way in, and the muffin will easily tear apart leaving lots of crags and dips for your butter or other toppings.