Warm the mixing bowl of an electric stand mixer by filling it with hot water and letting it sit for 5 minutes. Once the bowl is nice and warm, pour out the water and add the ½ cup hot water and the yeast to the bowl. Stir to combine. Let yeast mixture sit until bubbly and foaming, about 5 minutes, then add ½ cup flour. Stir well to combine and set in a warm place until batter rises up and then begins to fall. This will take anywhere from 40-60 minutes, depending on how warm your kitchen is.
Transfer the bowl to your mixer with dough hook attached. (If you don't have an electric mixer this can be done by hand. Use a strong wooden spoon for mixing.) Add eggs, sugar, salt, fresh thyme and lemon zest and remaining flour. Mix, with the dough hook, starting on low speed until most of the flour is incorporated, then increase speed to medium and mix for 5 minutes.
Add the soft butter and mix on a medium speed until it's fully incorporated and the dough is smooth and elastic, about 3-5 minutes. Scrape down the sides of the bowl once or twice during this mixing. Dough will look smooth and shiny. It will still be a bit sticky.
Cover dough with a clean towel and allow to rise in a warm place until doubled in size, 45 minutes to 1 hour. (May take a bit longer if you don't have a nice warm area for dough to rise.)
Spray 18 muffin cups with cooking spray.
Place the dough on a well-floured work surface. Turn the dough to coat with flour. Cut into 18 equal pieces, (about 2 ounces, or 60g each). Coat each piece with flour and form into smooth round balls. Place dough balls into the prepared muffin tins. Cover pans with clean kitchen towels, place in a warm area, and allow to rise until doubled in size, about 30-40 minutes.
During the last 15 minutes of rising time, preheat oven to 350˚F.
Combine egg and water and whisk vigorously to combine. Brush top of each roll with egg wash. Sprinkle lightly with sea salt.
Bake for 18-20 minutes or until golden brown. Cool on a cooling rack. Serve warm or at room temperature.