Preheat the oven to 350°F with a rack in the center. Line an 8" square pan with a parchment sling and lightly grease.
To make the cake: In a small bowl, stir together the water and oats and let sit for 20 minutes, uncovered, until the oats have absorbed the water.
Meanwhile, in a medium bowl, whisk together the flour, baking soda, salt, and cinnamon.
In a large bowl or the bowl of a stand mixer fitted with the flat beater, beat the butter and sugars until light and fluffy, 1 to 2 minutes on medium speed.
Add the eggs and vanilla to the butter mixture and mix until mostly combined, scraping the bowl as needed. The mixture may look slightly curdled at this point; that’s OK.
Add about half of the flour mixture and mix until combined. Scrape the bowl and then add the still-warm oatmeal to the batter. Mix to combine.
Add the remaining flour mixture to the bowl and stir until just combined, scraping the bowl as needed to ensure there are no dry bits remaining.
Transfer the batter to the prepared pan and spread into an even layer.
Bake the Oatmeal Cake for 30 to 35 minutes, or until the top is golden brown and feels set. About 5 minutes before the end of the bake time, prepare the topping.
To make the topping: In a small saucepan, combine the brown sugar, butter, and water. Cook the mixture over medium heat, stirring frequently, until the butter has melted, the sugar has dissolved, and bubbles start to form around the edges, 1 to 2 minutes. Add the pecans, coconut, and oats, and stir until well combined.
Remove the cake from the oven and place it on a wire rack to cool slightly. Set the oven to broil.
Carefully transfer the topping onto the baked Oatmeal Cake and spread it into a thin, even layer. Return the cake to the oven on the center rack and broil for 1 to 2 minutes, watching closely, or until the surface is bubbling and the pecans and coconut are lightly toasted.
Remove the cake from the oven and allow it to cool on the rack for 15 to 20 minutes before slicing and serving.