Optical resonators with high-quality factors (Q-factor) constitute the main building block for many photonic devices capitalizing on light-matter interactions, ranging from light emitters to biochemical sensors. While a high Q-factor enhances light-matter interactions, it also limits the device operation bandwidth. Here we propose and numerically analyze a generic coupling scheme to overcome the apparent trade-off. By using an orthogonal grating, broadband optical coupling into high-Q cavities of diverse geometric configurations can be achieved. As an example, the approach is applied to demonstrate over a 28-fold optical absorption enhancement across a 150 nm band around 900 nm wavelength in single-layer graphene embedded inside a Fabry-Perot cavity.