In an 8- to 10-inch nonstick frying pan over high heat, shake and tilt 1/2 cup granulated sugar until melted and amber-colored, about 4 minutes; be careful not to burn. At once, pour hot caramel onto a 12-inch foil square on a flat surface.
When caramel is cool enough to handle, peel off foil. Break caramel into chunks and put in a heavy plastic food bag. With a rolling pin or mallet, crush until largest chunks are about 1/4 inch.
In a large bowl, combine egg, applesauce, 1/4 cup butter, vanilla extract and brown sugar. With a mixer on medium-high speed, beat until well blended. Stir in flour, baking powder, baking soda, salt, and cinnamon; beat just until evenly moistened. Stir in caramel.
Scrape batter into a buttered 4 1/2 x 8 1/2-inch loaf pan about 6 1/2-cup capacity or equally into 2 buttered loaf pans, each 3 1/2 x 7 1/4 inches about 3-cup capacity.
Set pan on a sheet of foil placed on oven rack (to catch topping drips). Bake in a 350° F oven until bread is firm when pressed in the center, about 40 minutes for 61/2-cup pan and 30 minutes for 3-cup pans.
Meanwhile, in a small bowl, mix coconut with remaining 1/4 cup granulated sugar and 1/4 cup butter. When bread is firm to touch, spread mixture evenly over hot loaf or loaves. Continue to bake until coconut topping is evenly brown, 15 to 20 minutes.
Run a thin-bladed knife between bread and pan sides. Let bread cool in pan on a rack for about 10 minutes, then invert to release bread. Turn loaf rounded side up on rack. Let cool about 10 minutes. Slice to serve warm or at room temperature.
NOTES: As the bread bakes, the caramel chunks in the batter soften to form sweet lumps throughout. If making up to 1 day ahead, cool, wrap airtight, and store at room temperature; freeze to store longer.Servings: 1 loaf