Bring the water to about 95-105F (barely warm to touch) and pour into a mixing bowl. Add the yeast and the honey. Let the yeast hydrate for about 10 minutes, until you see foam forming on top.
Add the rest of the ingredients to the bowl, mix together and let rest for 20 minutes.
Knead the dough in the bowl for about 2 minutes. The dough should be soft and tacky to touch. Add more water if needed. If the dough feels too sticky, let it rest for another 10 minutes and then knead again for 1-2 minutes. As the flour in the dough absorbs more water and gluten develops stickiness will decrease. If you feel it is still too sticky, you can add more flour later when shaping rolls.
Cover the bowl with a damp kitchen towel or a plastic wrap and place in warm place for about 1 to 1.5 hours or until the dough doubles in size. A cold oven with the light on is a perfect place for this.
Cut the dough into 9 equal pieces. Shape each piece into a ball. Add some flour if the dough is too sticky. Place the dough balls into a greased round cake pan, spreading them out evenly.
Start preheating the oven to 360F (180C).
Cover the pan with a damp towel and let the dough balls proof for 40 minutes in a warm place.
Whisk one egg yolk in a small bowl. Using a pastry brush, paint the rolls with a light, even coat of egg wash.
Place the pan in the oven and bake for 25-30 minutes until golden brown. Sometimes, depending on how dry your oven runs, you may want to cover the pan with foil after 15 minutes of baking to avoid hardening of the top surface, or use a water pan to produce steady steam.
While your pampushki are baking, start making the garlic sauce. Press garlic into a medium bowl, add salt, oil, water, chopped herbs and stir. Set aside.
Once the pampushki are ready, transfer them to a serving platter. Drizzle the garlic sauce all over and let rest for a few minutes to allow the sauce to soak in. Serve warm.