For LLNs (Low power and Lossy Networks), RPL (IPv6 Routing Protocol for LLNs) has been standardized by the IETF (Internet Engineering Task Force) as a routing protocol for LLNs. In RPL, each node estimates the link quality to neighboring nodes and selects the parent node by the OF (Objective Function). As a result, a tree structure rooted at the sink is constructed. Existing OFs such as MRHOF (Minimum Rank with Hysteresis OF) adopt active monitoring for link quality estimation, i.e., each node periodically broadcasts control packets, which results in large control overhead. This paper proposes BROF (Broadcast Reception based OF) which employs passive monitoring for link quality estimation, i.e., each node estimates the link quality by the actual number of control packet receptions and the expected number of control packet receptions. This paper also evaluates the basic performance of BROF by comparing with MRHOF implemented in Contiki-NG, which is an OS (Operating System) for IoT devices. As a result, the number of parent node switching in BROF is 20% lower than that in MRHOF and the control overhead in BROF is 65% lower than that in MRHOF although the network construction time in BROF is 15% larger than that in MRHOF. Furthermore, the delay time of UDP packet transmission from each node to the sink in BROF is 1% smaller than that in MRHOF.