Rural Broadband Network Advancement Act of 2019 This bill establishes a program to collect fees for broadband network usage in rural areas and distribute them to rural broadband providers. Specifically, edge providers (online content or service providers such as search engines and streaming video platforms, so called because they are located at the edge of a network) that have their data transported through rural broadband providers in high-cost rural areas must pay network user fees. Such fees shall be distributed to eligible rural broadband providers for (1) deploying rural broadband networks, (2) operating and maintaining rural broadband networks, or (3) delivering broadband internet to users in high-cost rural areas.