To make the sponge: In a large bowl, dissolve the yeast and sugar in the warm water (make sure it’s warm – hot water will kill the yeast). Add 1 1/4 cups (162 g) flour and mix roughly. Cover with plastic wrap and leave to proof in the refrigerator overnight. The sponge should be bubbly and at least double in size after resting overnight.
The next morning: Add the remaining 1 1/4 cups (162 g) flour and the fine sea salt to the starter and knead on a well-floured work surface until the dough is smooth and comes away from your hands easily, 5 to 10 minutes.
Slick a 9-inch (23-cm) round baking dish or cake pan with oil. Divide the dough into 8 pieces and shape into round buns. Arrange them side by side in the prepared pan, cover with plastic wrap, and let them proof again, this time in a warm place, until doubled in size, 1 to 2 hours. They will join together just like hot cross buns do.
Meanwhile, preheat the oven to 425°F (220°C).
In a medium bowl, combine the crushed garlic, 3 tablespoons oil, a small pinch of sea salt, and the parsley. Stir well, then leave to infuse.
When the pampushky (the buns) look plump and ready, brush them generously with some beaten egg to glaze and bake until they form a glistening golden crust, 20 to 30 minutes.
Remove from the oven and baste with the garlic oil. Serve immediately.