In a small skillet, over medium heat cook the olive oil and thyme together until softened and fragrant but not browned. Set aside.
Stir together yeast and water in a small bowl and set aside for five minutes.
Heat the milk until warm, but not hot (about 110 degrees). In a large bowl whisk together the warm milk, vegetable shortening, sugar, salt, garlic and thyme. The shortening may not melt completely, but break it up into smaller pieces with your whisk.
Whisk in the yeast and egg. Add the flour and stir vigorously with a wooden spoon until dough forms.
Knead the dough on a lightly floured surface for 4-5 minutes until smooth and transfer to a lightly oiled bowl. Flip dough inside the bowl to coat with the oil, cover with plastic wrap and set in a non-drafty spot to rise until doubled in size, about 1 1/2 hours.
Brush down a 13 x 9 inch pan with a little melted butter and set aside.
Punch down the dough and divide into 4 equal pieces. On a lightly floured surface, roll the dough to into an 8x6 rectangle. Cut the dough into 3 strips -- 2" wide x 8" long. Cut those strips in half so you have 2"x4" rectangles. Brush dough with butter, pick up a strip of dough and fold the unbuttered side over on itself, leaving a little overhang. Place the dough in the corner of the pan, with the folded side facing the short end of the pan. Fill the pan short side first and continue with the rest of the dough. Lightly brush with butter, cover and refrigerate for half an hour.
Preheat oven to 350 degrees.
Remove plastic wrap and bake rolls until golden brown, about 30-35 minutes. Lightly brush with butter and sprinkle with additional thyme leaves and sea salt. Serve.