Activate the yeast: Combine the active dry yeast, sugar, and warm water. Let it sit for 5 to 10 minutes, until foamy. If using instant yeast, skip this step and add it to the flour.
Mix the dry ingredients: Whisk together the bread flour and salt. If using instant yeast, add it here.
Mix the wet ingredients: Into the yeast mixture, add the egg, condensed milk, and oil. Mix until smooth. If using instant yeast, combine the egg, condensed milk, oil, water, and sugar in a separate bowl.
Make the dough: Pour the wet ingredients into the dry ingredients. Mix until a sticky dough forms.
Knead: Knead with a dough hook for 12 to 15 minutes or by hand for 20 to 25 minutes. The dough should become smooth and stretchy and come together into a soft ball.
Let it rise: Place the dough in a lightly greased bowl and cover it. Let it rise in a warm place for 1 to 2 hours, or until doubled in size.
Make the filling: Mix the softened butter, brown sugar, breadcrumbs, vanilla, and a pinch of salt (if using unsalted butter).
Divide and fill: Divide the dough into 16 pieces. Flatten each piece into a 6-by-3-inch oval. Add about 2 tablespoons of filling, leaving a small border around the edges.
Shape and coat: Roll each piece into a log and pinch the seam closed. Roll it in the breadcrumbs and place it seam-side down on a parchment-lined baking sheet.
Let them rise: Cover and let the rolls rise for 30 to 45 minutes, or until puffy.
Bake: Bake at 400°F (205°C) for 5 minutes. Lower the temperature to 350°F (175°C) and bake for another 13 to 15 minutes, or until lightly golden.
Let the rolls cool for a few minutes. Serve warm or at room temperature.