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Combine the leftover cooked oatmeal, warm water, agave syrup, and 1 tablespoon of oil in a large mixing bowl. Add the dry mixture to the cooked oatmeal mixture in 3 installments and mix thoroughly with a wooden spoon after each addition.
Turn the dough onto a lightly floured surface, and knead by hand for 10 minutes, incorporating more flour, if needed. Dough will be sticky. Put the dough in a lightly oiled bowl or container. Cover with plastic wrap and set in a warm place to rise until the dough has doubled in size, about 1 hour.
Heat the oven to 350 degrees F.
Combine the egg yolk and water in a small bowl. Lightly brush the top of the loaf with egg wash and sprinkle with remaining 1 tablespoon toasted, uncooked oats. Bake until the bread reaches an internal temperature registers 210 degrees F on an instant-read thermometer, about 55 minutes to 1 hour. Remove the loaf from the pan to a cooling rack for 30 minutes before slicing and serving.