In a small bowl mix the ginger, lemongrass, garlic, thyme, and Jalapeño or Fresno pepper. Add soy sauce, oyster sauce, and honey. Taste and adjust with kosher salt and black pepper. (See notes.)
Put each turkey leg into a 1 gallon resealable bag. (Unlikely that these would fit into a 1-quart bag well.)
Spoon the cooking mixture over each leg equally. Squish the legs around in the bag to coat evenly.
Add the rosemary. Add weights if you'd like. Remove the air from the bags by your preferred method.
Fill your immersion cooker vessel to cover the legs and get well above the minimum line of your immersion cooker. (My container has a lid -- if yours doesn't, cover with plastic wrap and/or foil and check the water level often as evaporation will be happening.)
Set your immersion cooker for 150°F / 65°C and 24-30 hours. (For example, I started mine at 2pm on the day before Thanksgiving so that we could eat pretty much any time Thanksgiving afternoon.)
At the end of the immersion cooking, remove the legs from the bags and discard the marinade/cooking liquid.
Heat a pan on medium-high heat. When hot, add 1 tablespoon of oil and immediately add the legs facing opposite directions so that they'll both fit. If you don't have a large enough pan you may need to sear them separately. Sear for 1-2 minutes per side, turning as needed.