In a shallow bowl, sprinkle yeast on top of the water. Let stand 5-10 minutes, until foamy.
In an electric mixing bowl, combine proofed yeast with butter, salt, 1/4 cup of the sugar and 1 cup of flour. Using a dough hook, mix until well combined.
Add remaining flour and knead for 5 minutes, until dough is elastic. Place in a lightly greased bowl. Cover with plastic wrap sprayed with non stick spray and a kitchen towel. Leave to rise until doubled in size, 60 - 75 minutes.
Meanwhile, let's make the filling. In a saucepan, combine the apricots, remaining sugar and water. Bring to a boil. Reduce heat and simmer, stirring occasionally, until apricots are softened, about 15 - 20 minutes. Using a slotted spoon, remove apricots to a bowl.You should have about 1/3 cup of syrup remaining in pot.
Preheat oven to 375 F.
Punch dough to remove air. Press dough into the bottom and sides of a tart pan with a removable bottom.
Arrange apricots, slightly overlapping, over the surface of the dough. Pour syrup on top. Gently press down down so that it is flush with the fruit.
Bake for 35 - 40 minutes, until crust is golden brown.