Whisk together the yogurt, 1/4 cup of the milk, and 2 tablespoons of the honey in a medium bowl. The yogurt should be thick but pourable, roughly the consistency of regular yogurt. If needed, whisk in a little more milk. Taste and add more honey, if desired.
Scoop out 1/4 cup of the yogurt mixture and stir it into the granola. This helps the granola freeze into the popsicles.
Arrange six popsicle molds (1/2 cup capacity each) on your work surface. Pour a generous spoonful of yogurt into the bottom of each mold. Add a scoop of granola, then a spoonful or two of jam. Continue layering yogurt, granola, and jam until the molds are filled.
Tap the molds lightly against the counter, or use a popsicle stick, to work out any air bubbles between the layers. Insert a popsicle stick into each mold.
Freeze until solid, at least six hours.
To unmold, run the molds under hot running water for a few seconds and gently ease the popsicles out.