For the Dough: In a stand mixer bowl fitted with the paddle attachment (or a large mixing bowl if kneading by hand), combine the egg, 2.25 cups flour, granulated sugar, oil, yeast, and salt. Set aside.

Warm the milk in a glass measuring cup (about 45 seconds on high power in the microwave) to approximately 110-115°F. Be careful not to make it too hot, as it can kill the yeast.

Pour the warm milk over the dry ingredients in the mixer bowl. Knead on low speed for about 7 minutes (or 10 minutes by hand) until the dough starts to pull away from the sides of the bowl. If the dough is very sticky after 5 minutes, add the remaining 0.25 cup flour, 1 tablespoon at a time, until the dough is no longer excessively sticky but still tacky.

Turn the dough out into a large, greased bowl, cover with plastic wrap, and let it rise in a warm, draft-free place for about 2 hours, or until doubled in size. An ideal warm spot can be created by preheating your oven to 400°F for 1-2 minutes, then turning it off.

Punch down the risen dough and turn it out onto a lightly floured surface. Knead for about 3 minutes.

For the Filling: Spray a 9 or 10-inch pie plate or baking dish with cooking spray. Roll the dough into an 18-inch by 12-inch rectangle.

Spread the softened butter evenly over the surface of the dough, leaving a small margin around the edges.

Spread the strawberry preserves or jam evenly over the butter.

Starting with a long side, roll the dough into a tight cylinder.

Slice the cylinder into 8 to 10 evenly sized pieces (about 2 inches wide) using a bench scraper, serrated knife, or unwaxed dental floss. Arrange the rolls in the prepared baking pan.

Cover the pan with plastic wrap. At this point, you can either let the rolls rise at room temperature for about 60-75 minutes until nearly doubled, or refrigerate them for up to 18 hours (make-ahead option). If refrigerating, let them rise in a warm place for 60-75 minutes before baking.

In the last minutes of rising, preheat your oven to 350°F.

Bake at 350°F for 25 to 30 minutes, or until lightly golden brown and cooked through. If the tops are browning too quickly, you can loosely tent with foil.

While the rolls are baking, prepare the glaze. In a small bowl, combine the softened cream cheese, granulated sugar, softened butter, and vanilla extract. Beat with a whisk or mixer until smooth.

Once the rolls are baked, generously drizzle the cream cheese glaze over the warm rolls. Serve immediately. Rolls are best enjoyed fresh but can be stored in an airtight container at room temperature for up to 4 days.