We have been doing low CFM recirculating hoods for grease and odor filtration, so I will expand on that subject here but touch on other options as well.
Ideally, the ventilation of the Passive House kitchen (and home) is delivered by the balanced, whole-house heat recovery ventilation system and not augmented with a make-up air/ extract system. We follow PHI guidance for return air grate placement in the kitchen and always put a local filter into that return air register. Good range hoods have stainless steel grease filters that can be cleaned in the dishwasher. Odor filtration is commonly accomplished with a charcoal filter, which needs replacement over time. In our market, we are able to find both decorative island hoods, as well as under-cabinet hoods that work in this way.
In Minnesota, make-up air is required by code when installing an exterior-vented range hood over 600 CFM (check me on the numbers). We have done these systems but not on Passive House buildings as that approach is counter-intuitive in regards to energy consumption (make-up air means 100% heating of outside air, which can be as cold as -30 C/ -22 F). However, a system like that could be devised for a PH (hopefully with a smaller CFM load) if a Client absolutely insisted on exhausting the range hood directly. In this case, the controls need to be structured so that the make-up air system runs as briefly as possible and the intakes and exhausts are dampered. I think this presents risks of condensation at those damper locations and the entire duct network would have to be insulated and vapor-barriered thoroughly. Likely a liability, which is why we educate clients and go the other route. I don't have specific equipment recommendations as we stopped providing these systems years ago since we feel that they are too much of a risk factor in our climate zone. We also had one experience with a client where they forgot to turn their hood off after cooking a big meal. It (and the make-up air system) ended up running for an extended period of time during Minnesota's cold winter, consuming literally hundreds of kWh and shocking the client when receiving the next electric bill. Ouch!
Options: Some ventilators offer an "over-supply" of outside air for such purposes. Usually, they can only provide a small CFM amount and a preheater would be needed in our cold climate as the lack of heat recovery power on a cold day would overwhelm the machine. The kitchen range hood would then have to relay a start and stop signal to the ventilator to "pressurize" the home during exhaust mode. I think Zehnder ventilators generally have ports to trigger this.
Zehnder has a partnership with a Swiss manufacturer who makes an integrated solution where the range hood does not have a built-in fan, but instead controls the ventilator fans to perform the suction, and the machine's core to provide heat recovery during cooking. In this case, the range hood again becomes a filter and essentially a big return air inlet. During cooking, all return air from the home is diverted to the ventilation system via a damper in the main trunk. We contacted the manufacturer in past years but they do not wish to sell their product in the USA. We are aware of 2 installations in the country that were done by simply purchasing equipment in Europe and bringing it here. However, this can cause code challenges and obviously there isn't any support. Also, the hood alone retails for over $4,000 last we checked, so it is very expensive.
Let me know if you have follow up questions.