Pour warm water into the bowl of a stand mixer fitted with a dough hook attachment. Sprinkle the yeast and 1/2 tsp brown sugar on top of the water. Stir it lightly with a spoon and allow to sit for a few minutes until the mixture is frothy and smells like yeast. (If that's not happening, start over with new yeast.)
With the mixer running on low speed, add the remaining brown sugar, salt, oil, and 3 cups of bread flour. Beat on low speed for 2 minutes as it all combines. The dough should be thick, yet soft and only slightly sticky. When it pulls away from the sides of the bowl it's ready to knead.
Form dough into a ball and turn it out onto a lightly floured surface. Knead for 2 minutes, then place in a greased bowl and turn the dough over to coat all sides. Cover the bowl with plastic wrap and place it in a warm environment to rise until doubled, about 1-2 hours.
Once doubled in size, punch the dough down to release any air bubbles. Remove dough from the bowl and turn it out onto a lightly floured surface. Divide the dough into 10 equal pieces.
Heat oven to 350°F. Line your cookie sheet with cooking parchment paper, or lightly grease the cookie sheet.
If you want to add a little bit of Italian seasoning to your dough, now it's the time. Roll each ball of dough into a rope 12 inches long. Two of these ropes will be the shamrock stems, cut these both in half so you have 4 stems.
It's best to shape the shamrocks on the prepared cookie sheet. Pinch the ends of a rope together in the center of the rope to form two circles, form another rope in the same way, then pinch the two formed ropes together to make a shamrock shape (See picture below). Press on stem piece in the base of the shamrock shaped bread. Repeat this process to make a total of four shamrock breads.
Brush the shamrocks with egg white and sprinkle coarse sea salt and Italian seasoning on top of each shamrock.
Bake 15 - 20 minutes or until golden brown (Each oven is a little bit different so have an eye on your baked goods). Serve with cream cheese to dip or as a side dish for dinner!