If your application is small, I would use a base controller that extends the template controller.
In the before method of this controller, I would define the page template, and all static sections of the template. Have your application controller extend this base controller. In its before method, call the parent, and then have it set all sections that are the same for all methods in that controller. And set the remaining sections, the dynamic ones, in the controller methods.
If your application is a bit bigger, you might want to look at the Theme class, which gives you more functionality when it comes to page templates. It is loosely modelled on Joomla's theme layout, and supports multiple views per section, section chrome (for example borders around your entire sidebar), themes with fallback, etc.
Same if you need more flexibility, for example if you have multiple page templates, a front-end with a different layout from your admin section, etc.
Ok, then the same method applies, but the base controller should extend the normal controller, not the template controller, and it it's after method, return a response with the theme object in it.