For the challah: In a medium bowl, combine the warm water, yeast and 1 teaspoon granulated sugar and give it a little stir. Let it sit until it becomes foamy on top, about 5 minutes.
Meanwhile, in a large bowl or the bowl of stand mixer fitted with a dough hook, mix together the flour, salt and remaining 1/4 cup granulated sugar. In a separate medium bowl, whisk together the oil and eggs.
When the yeast is foamy, add it to the dry mixture immediately followed by the egg mixture and stir to combine. Knead, either by hand on a floured surface or with a dough hook, adding more flour as necessary (but resist any urge to add too much!), until you have a smooth and slightly sticky dough, 7 to 10 minutes. Transfer the dough to an oiled bowl, cover it with plastic wrap and let it sit at room temperature until it has doubled in size, about 2 hours.
For the filling: In a medium bowl, mix together the granulated sugar and butter with a wooden spoon or rubber spatula until combined. Mix in the salt and egg white (reserve the egg yolk for the egg wash), and then add the vanilla extract. Stir in the pecan flour.
Line 2 baking sheets with parchment paper.
When the dough has risen, turn it out onto a clean surface (dust with a little flour if it's too sticky) and divide into 14 balls. Fill each ball with a heaping tablespoon of filling and seal well to shut. Place the balls seam-side down on the lined baking sheets, spaced evenly apart. Let rise for 30 more minutes.
Preheat the oven to 375 degrees F.
In a small bowl, beat the reserved egg yolk with a splash of water. Working with 3 rolls at a time, brush the egg wash onto the rolls, use scissors to make two 1/2-inch cuts for ears and use tweezers to stick on 2 black sesame seeds for eyes. (If you wait too long after brushing on the egg wash, it will dry and the sesame seeds won't stick; that's why you want to work with no more than 3 rolls at a time.)
Bake until golden brown; begin checking for doneness at 20 minutes.
For the glaze: In a small bowl, mix together the powdered sugar, almond extract and 5 teaspoons milk. If it's too thick to spread, add additional milk, a couple of drops at a time, until it's spreadable.
Working one at a time, spread a circle of glaze onto the rolls and then top with overlapping rows of slivered almonds.