In a 3-quart / 2.8 L bowl, whisk 300 g flour, 4 g yeast, 35 g sugar, 1/2 tsp salt, and 1 tbsp poppy seeds. Add 140 ml warm water (38 C / 100 F), 40 ml oil, and 1 tbsp honey. Stir into a shaggy dough, then knead on a lightly floured counter for 8 minutes until firm, smooth, and no longer sticky. If it cracks, work in 1 tbsp water.
Cover the bowl and let the dough rise for 45 minutes in a warm spot, until it puffs to about 1.5 times its size.
While the dough rises, grind 120 g poppy seeds in a spice grinder in 4 batches of 20-second bursts, until powdery. Tip the powder into a 1.5 L / 6-cup heatproof bowl, pour over 250 ml boiling water, stir, cover, and leave for 30 minutes.
Heat the oven to 180 C / 350 F and line two sheet pans, 33 x 46 cm / 13 x 18 inch, with parchment. Divide the risen dough into 8 pieces of about 70 g. Roll each into a 20 cm / 8-inch rope about 2 cm / 3/4 inch thick and cut it into ten 2 cm pieces, for about 80 bites.
Whisk 1 tbsp honey with 1 tbsp warm water in a bowl. Add the bites and toss to coat, then sprinkle over 1 tbsp poppy seeds and toss again. Spread the bites on the pans, about 1 cm / 1/2 inch apart.
Bake for 14 minutes at 180 C / 350 F, swapping the pans between racks halfway, until light golden. Lower the oven to 120 C / 250 F and bake 20 minutes more, until the bites feel dry and hard. Snap one open to check for a dry, pale crumb.
While the bites bake, stir 350 ml hot water and 3 tbsp honey into the soaked poppy seeds. Whisk for 1 minute until the milk turns pale gray and cloudy, then leave it at room temperature.
Cool the bites on the pans for 15 minutes so they firm up. Whisk the poppy milk again, spoon about 120 ml into each bowl, add about 13 bites, and wait 2 to 3 minutes before eating.