Fill a small saucepan with water and place over high heat. Bring the water to a boil and reduce to a simmer. Add the baking soda to the water and lower the eggs in. Cook for 6-7 minutes.Transfer the eggs to an ice water bath and let sit for at least 10 minutes.
While the eggs are chilling, pour the water and vinegar into a small saucepan. Add the salt, honey and mustard seeds and place the pan over high heat. Bring the mixture to a boil. Cook until the salt and honey have dissolved completely. Take the saucepan off of the heat and set aside.
Peel the eggs and layer them into a mason jar alternating between handfuls of radish slices. Add the cloves of garlic to the jar and pour the vinegar solution over top. Seal the jar and let cool at room temperature before transferring to the fridge. Let the eggs pickle for 24 hours before eating.