• Combine the warm water, yeast, and 1 tablespoon sugar in a small bowl. Let it stand for 5 to 10 minutes, or until the yeast looks foamy.
  
• In the bowl of a stand mixer, combine the warm milk, melted butter, ½ cup sugar, and salt. Make sure the mixture is warm but not hot before adding the eggs.
  
• Add the eggs and 3 cups of the flour. Mix for about 2 minutes, scraping the sides of the bowl as needed.
  
• Add the yeast mixture and another 2 cups of flour. Mix until combined, then let the dough rest for 10 minutes. Switch to the dough hook attachment.
  
• Knead on low speed while gradually adding the remaining flour, about ½ cup at a time. Add only enough flour for the dough to begin pulling away from the sides of the bowl. The dough should be very soft and slightly tacky, not stiff or dry. Continue kneading for 3 to 5 minutes.
  
• Coat a large bowl with the vegetable oil. Place the dough in the bowl and turn it once to coat.
  
• Cover with a clean towel or plastic wrap and let it rise in a warm place for 45 to 60 minutes, or until doubled in size.
  
• Grease a 13-by-18-inch rimmed baking sheet. Gently press the air out of the risen dough and place it on a lightly floured surface. Roll it into a rectangle approximately 13 by 18 inches. If the dough keeps springing back, let it rest for 5 minutes before continuing.
  
• Spread 1/3 cup softened butter evenly over the dough, leaving about a ½-inch border along one long edge. Combine the granulated sugar, brown sugar, and cinnamon in a small bowl. Sprinkle the mixture evenly over the butter.
  
• Place the peach slices between layers of paper towels and gently press out as much moisture as possible. Transfer the peaches to a bowl and toss them with the cornstarch until lightly and evenly coated.

  Arrange the peach slices evenly over the cinnamon-sugar mixture. Keep them in a fairly even layer rather than piling them on top of one another. Sprinkle with sliced almonds, if using.
  
• Starting with the long side, roll the dough into a snug log. Roll firmly enough to hold everything together, but do not squeeze the peaches out of the dough. Pinch the seam closed.
  
• Cut the log into 15 equal pieces, approximately 1¼ inches wide. Unflavored dental floss works especially well for cutting the rolls without flattening them.

  Arrange the rolls on the prepared baking sheet. Cover and let them rise for 25 to 35 minutes, or until noticeably puffy. They do not need to double in size.
  
• While the rolls are rising, preheat the oven to 350℉.

  Bake for 22 to 27 minutes, or until the tops are golden brown and the center rolls are fully baked. The center of the rolls should register approximately 190 degrees F on an instant-read thermometer. If the tops begin browning too quickly, loosely cover them with foil for the remaining baking time.

  Let the rolls cool for at least 10 minutes before frosting.
  

For the frosting:

• Beat the softened cream cheese and butter together until smooth. Add the almond extract and vanilla and mix again.

  Gradually add 3 cups of powdered sugar. Add the milk or cream 1 tablespoon at a time until the frosting reaches your desired consistency. Add more powdered sugar if you prefer a thicker frosting.
  
• Spread or pipe the frosting over the warm cinnamon rolls and serve.