Into the bowl with the activated yeast mixture, add the egg, flour remaining sugar and salt. With the dough hook attached, mix together the dough ingredients at low speed just until a dough starts to form.

Mix in the butter a little at a time. Once the butter is fully incorporated into the dough, increase mixer speed to medium and knead the dough for 5-6 minutes. The resulting dough should be smooth and slightly tacky to touch.

Using lightly greased hands, transfer the dough into a greased mixing bowl, cover with plastic wrap and set aside in a warm area to rise until doubled in size, about 60-90 minutes.

Lightly grease a 9 x 9 inch square baking pan and line with parchment paper. Set aside.

Deflate risen dough and transfer onto a lightly floured surface. With a bench scraper or sharp knife, cut the dough into 8 equal pieces.

Working with one piece of dough at a time, use hands or a rolling pin to shape into a rectangle measuring about 4 x 5 inches (does not need to be precise).

Starting on the short end of the rectangle, roll the dough onto itself into a log shape. Transfer into prepared baking dish and repeat with remaining pieces of dough.

Cover baking dish with plastic wrap and set the pan in a warm area to allow the Texas toast rolls to undergo a second rise for 25-35 minutes or until doubled.

As the Texas toast rolls rises, preheat the oven to 350F. Prepare egg wash by whisking together the egg and water in a small dish. Use a pastry brush to apply the egg wash over the risen dough. Sprinkle the top with some sesame seeds.

Bake the Texas toast rolls for 25-30 minutes, rotating the pan halfway through bake time for even baking. The rolls are ready when a toothpick inserted into one of the rolls comes out clean and it is has a rich golden brown color.

Brush the tops of the Texas toast rolls with melted butter fresh out the oven and serve warm as is or toasted in butter (highly recommend). Enjoy!