When designing a new API for a large project, developers need to make smart design choices so that their code base can grow sustainably. To ensure that new API components are well designed, developers can learn from existing API components. However, the lack of standardized methods for comparing API designs makes this learning process time-consuming and difficult. To address this gap we developed API-Miner, to the best of our knowledge, one of the first API-to-API specification recommendation engines. API-Miner retrieves relevant specification components written in OpenAPI (a widely adopted language used to describe web APIs). API-miner presents several significant contributions, including: (1) novel methods of processing and extracting key information from OpenAPI specifications, (2) innovative feature extraction techniques that are optimized for the highly technical API specification domain, and (3) a novel log-linear probabilistic model that combines multiple signals to retrieve relevant and high quality OpenAPI specification components given a query specification. We evaluate API-Miner in both quantitative and qualitative tasks and achieve an overall of 91.7% recall@1 and 56.2% F1, which surpasses baseline performance by 15.4% in recall@1 and 3.2% in F1. Overall, API-Miner will allow developers to retrieve relevant OpenAPI specification components from a public or internal database in the early stages of the API development cycle, so that they can learn from existing established examples and potentially identify redundancies in their work. It provides the guidance developers need to accelerate development process and contribute thoughtfully designed APIs that promote code maintainability and quality. Code is available on GitHub at https://github.com/jpmorganchase/api-miner.