HTTP/3 is a new application layer protocol supported by most browsers. It uses QUIC as an underlying transport protocol. QUIC provides multiple benefits, like faster connection establishment, reduced latency, and improved connection migration. Hence, most popular browsers like Chrome/Chromium, Microsoft Edge, Apple Safari, and Mozilla Firefox have started supporting it. In this paper, we present an HTTP/3-supported browser dataset collection tool named H3B. It collects the application and network-level logs during YouTube streaming. We consider YouTube, as it the most popular video streaming application supporting QUIC. Using this tool, we collected a dataset of over 5936 YouTube sessions covering 5464 hours of streaming over 5 different geographical locations and 5 different bandwidth patterns. We believe our tool and as well as the dataset could be used in multiple applications such as a better configuration of application/transport protocols based on the network conditions, intelligent integration of network and application, predicting YouTube's QoE etc. We analyze the dataset and observe that during an HTTP/3 streaming not all requests are served by HTTP/3. Instead whenever the network condition is not favorable the browser chooses to fallback, and the application requests are transmitted using HTTP/2 over the old-standing transport protocol TCP. We observe that such switching of protocols impacts the performance of video streaming applications.