In the bowl of a stand mixer, or other large bowl, sprinkle yeast into warm water with 1 tablespoon of sugar. Let proof until foamy and bubbly on top.
Meanwhile, mince garlic. Sprinkle salt over garlic and continue to chop, scraping your knife over it firmly until it forms a chunky paste. Set aside.
When yeast is ready, fit onto stand mixer fitted with dough hook and add in remaining sugar and 1 of the eggs beaten. Turn on mixer or mix by hand to combine.
Add in the flour in three parts until fully incorporated. Next mix in the softened butter and garlic, kneading until dough pulls away from bowl and is smooth but tacky. About 4-5 minutes on a stand mixer or 10 minutes by hand.
Form dough into ball and place in well oiled bowl, turning to coat. cover with plastic wrap or a clean towel and allow to rise until doubled in volume, about 1 hour.
Punch down dough and turn out onto lightly floured work surface. Divide dough into 15 equal pieces. Pull edges of each piece and pinch at bottom. Use the palm of your hand and gently place the ball seam side down on work surface and roll to form ball.
Place balls on parchment lined baking sheet 1 inch apart. Cover and let rise again until doubled, about 1 hour.
Preheat oven to 350°F, and beat second egg with 2 teaspoons of water. Brush tops of rolls gently with egg wash and place in preheated oven. Bake 17-20 minutes.
When rolls are golden brown remove from oven and place on cooling rack. Serve warm or store in an airtight container or bag for up to 3 days. Freeze in sealed container for up to 4 months.