Pour the sun-dried tomato through a strainer to remove the oil. Pat dry the tomato pieces. We don't need the oil.
Preheat oven to 400 degrees F.
Line a baking pan with parchment paper.
Cube the cheese, about ¼”. Shredding causes the cheese to disappear into the mix too much!
In a stand mixer using the dough hook, or by hand in a large bowl, combine flour, sugar, baking powder, cheese, tomato, and salt. Add cold butter cubes. Mix to work the butter into the dry ingredients, until it resembles coarse crumbs.
Pour in ¾ of the heavy cream, and mix until a soft dough just forms. Add more if needed. Hold back 2 tbs.
Place on a lightly floured surface, knead the dough several times, until it comes together.
Roll into a 10” circle, no more than 1/2-inch thick. Too thick and the baking time goes up, to bake the inside.
Cut into 8 wedges and separate them. Place on the baking sheet.
Brush some cream over them.
Bake for 20 min, then cover with aluminum foil. Cut a narrow triangle slice from one of the wedges, to see how wet the interior remains. Bake 5-10 min more, until the interior still shows a slight dampness, until the top is firm to the touch and lightly browned.
For left-overs, re-heat at 250 degrees for 8 minutes.