In a small saucepan, combine the yogurt, sugar and butter. Heat over low heat, stirring occasionally, until butter is melted and ingredients are well combined. Remove from heat and cool to room temperature.
Place cooled yogurt mixture in a medium bowl and add the water, salt, yeast (if instant) and flour. Mix well. Dough will be very soft. Cover and refrigerate overnight. If using ADY, add the warm water and yeast to the bowl FIRST and dissolve yeast. Proceed as above.
Preheat oven to 375 degrees F. Lightly grease Revol Basalt Round Pan or any 12-inch pizza pan.
Punch down dough and turn out on a lightly floured surface. Knead a few times until smooth. Roll out dough in a 14-inch circle. Transfer to prepared pizza pan. Roll up the overhang so it makes a "wall" around the perimeter of the pan, like a pizza crust.
Prepare filling by beating the cream cheese (or Neufchatel), egg, salt and almond extract. Beat well so there are no lumps.
Spread filling in center of crust, up to the "walls." Top with lightly toasted sliced almonds.
Bake at 375 degrees F for 20-25 minutes or until filling is puffy and walls of crust are lightly browned. Remove from oven and cool completely.
For icing, mix confectioner's sugar and extract. Add cream tablespoon by tablespoon until icing is of a thick, but pourable consistency (I used an icing bag with a small round tip, so my icing was a bit stiffer than the usual "liquidy" kind). Drizzle over completely cooled pizza, or use a piping bag with a small round tip.