The Border Gateway Protocol (BGP) was designed almost three decades ago and has many limitations relating to its fully distributed nature, policy enforcement capabilities, scalability, security and complexity. For example, the control plane can take several minutes to converge after a routing change; this may be unacceptable for real-time network services. Despite many research proposals for incremental improvements and clean-slate redesigns of how inter-domain routing should work, BGP is likely one of the most ossified protocols of the Internet architecture and it has not retrofitted the proposed ideas. In this work, we propose a radical, incrementally deployable Internet routing paradigm in which the control plane of multiple networks is logically centralized. This follows the Software Defined Networking (SDN) paradigm, although at the inter-domain level involving multiple Autonomous Systems (AS). Multi-domain SDN centralization can be realized by outsourcing routing functions to an external contractor, which provides inter-domain routing services facilitated through a multi-AS network controller. The proposed model promises to become a vehicle for evolving BGP and uses the bird's eye view over several networks to benefit aspects of interdomain routing, such as convergence properties, policy conflict resolution, inter-domain troubleshooting, and collaborative security. In addition to the proposed paradigm, we introduce a publicly available emulation platform built on top of Mininet and the Quagga routing software, for experimenting on hybrid BGP-SDN AS-level networks. As a proof of concept, we focus specifically on exploiting multi-domain centralization to improve BGP's slow convergence. We build and make publicly available a first multi-AS controller tailored to this use case and demonstrate experimentally that SDN centralization helps to linearly reduce BGP convergence times and churn rates with expanding SDN deployments.