We introduce BULLKID, a phonon detector consisting of an array of dices acting as particle absorbers sensed by multiplexed Kinetic Inductance Detectors (KIDs). The dices are carved in a thick crystalline wafer and form a monolithic structure. The carvings leave a thin common disk intact in the wafer, acting both as holder for the dices and as substrate for the KID lithography. The prototype presented consists of an array of 64 dices of 5.4 × 5.4 × 5 mm³ carved in a 3˝ diameter, 5 mm thick silicon wafer, with a common disk of 0.5 mm thick, hosting a 60 nm patterned aluminum layer. The resulting array is highly segmented but avoids the use of dedicated holding structures for each unit. Despite the fact that the uniformity of the KID electrical response across the array needs optimization, the operation of eight units with similar features shows, on average, a baseline energy resolution of 26 ± 7 eV. This makes it a suitable detector for low-energy processes such as direct interactions of dark matter and coherent elastic neutrino-nucleus scattering.