RNA sequencing (RNA-seq) is widely adopted for transcriptome analysis but has inherent biases that hinder the comprehensive detection and quantification of alternative splicing. To address this, we present an efficient targeted RNA-seq method that greatly enriches for splicing-informative junction-spanning reads. Local splicing variation sequencing (LSV-seq) utilizes multiplexed reverse transcription from highly scalable pools of primers anchored near splicing events of interest. Primers are designed using Optimal Prime, a novel machine learning algorithm trained on the performance of thousands of primer sequences. In experimental benchmarks, LSV-seq achieves high on-target capture rates and concordance with RNA-seq, while requiring significantly lower sequencing depth. Leveraging deep learning splicing code predictions, we used LSV-seq to target events with low coverage in GTEx RNA-seq data and newly discover hundreds of tissue-specific splicing events. Our results demonstrate the ability of LSV-seq to quantify splicing of events of interest at high-throughput and with exceptional sensitivity.