In the bowl of a mixer fitted with the dough-hook attachment, combine yeast, 3/4 cup warm water (110 degrees), and pinch of sugar. Let stand until foamy, about 5 minutes. Beat on low speed while adding 2 tablespoons oil, salt, and 1 teaspoon sugar. Slowly add flour while beating until mixture just comes together. Increase speed to medium-high; beat until dough is soft and elastic, 3 minutes.

Coat a 9-by-13-inch metal baking pan with 3 tablespoons oil. Transfer dough to pan; press to edges with your hands (being careful not to tear). Cover with plastic wrap and let rise in a warm place until doubled in bulk, about 1 hour.

Preheat oven to 425 degrees with a rack in lower third. Press dimple-like indentations all over dough with your fingers. Stir together cream cheese and remaining 2 tablespoons sugar; dot all over dough. Arrange 12 apricot halves on top in a 3-by-4 grid formation. Drizzle with remaining 1 tablespoon oil. Cover with plastic wrap and let rise in a warm place until puffed, 30 minutes.

Bake until golden brown on top, 23 to 25 minutes. Let cool in pan 10 minutes, then transfer with two large spatulas to a wire rack. Drizzle with honey and oil; let cool completely. Cut into squares and serve.