We explore signals of new physics with two Higgs bosons and large missing transverse energy at the LHC. Such a signature is characteristic of models for dark matter or other secluded particles that couple to the standard model through an extended scalar sector. Our goal is to provide search strategies and an interpretation framework for this new signature that are applicable to a large class of models. To this end, we define simplified models of hidden sectors leading to two different event topologies: symmetric decay, i.e., pair-produced mediators decaying each into a Higgs plus invisible final state; and di-Higgs resonance, i.e., resonant Higgs-pair production recoiling against a pair of invisible particles. For both scenarios, we optimize the discovery potential by performing a multi-variate analysis of final states with four bottom quarks and missing energy, employing state-of-the-art machine learning algorithms for signal-background discrimination. We determine the parameter space that the LHC can test in both scenarios, thus facilitating an interpretation of our results in terms of complete models. Di-Higgs production with missing energy is competitive with other missing energy searches and thus provides a new opportunity to find hidden particles at the LHC.