Place the water, sugar and salt in the bowl of an electric mixer and sprinkle the yeast on top of the water. Let it foam for 5-10 minutes.

Using the dough hook, add the 4 1/2 cups flour and the melted butter into the yeast mixture and mix on low speed until well combined. Change to medium speed and knead until the dough is smooth and pulls away from the side of the bowl, approximately 5-6 minutes.

Remove the dough from the bowl, spray the bowl with nonstick spray, then place the dough back in the bowl, cover with plastic wrap and set the bowl in a warm place for approximately 1 hour or until the dough has doubled in size.

Meanwhile, prep the apples and put them in a small bowl. Add the cinnamon, nutmeg and 1 tablespoon of flour. After the dough has doubled, pour the apples into the dough and knead to combine.

Preheat the oven to 450 F. Line 2 cookie sheets with parchment paper and spray with nonstick spray. Set aside.

Bring the 3 quarts of water and the baking soda to a boil in a large sauce pot.

In the meantime, dump the dough out onto a slightly floured work surface and divide into 8 equal pieces (or 16 pieces for mini pretzels.)

Spray a work surface with nonstick spray. Roll out each piece of dough into a 24-inch rope (12-inch for minis.) The apples will pop out a little, but keep rolling and you will reincorporate them.

Make a U-shape with the ropes. Take the ends and cross them over each other twice, and press the ends onto the bottom of the U to form the pretzel. Place pretzels onto the parchment-lined sheets.

Beat the egg yolk and 1 tablespoon of water in a shallow bowl and set aside.

Put the pretzels into the boiling water, one at a time, for 30 seconds. Remove from the water using 1-2 large spatulas. Return them to the cookie sheet and brush each pretzel with the beaten egg yolk and water mixture.

Bake until dark golden brown, 12 to 14 minutes.

Transfer to a cooling rack and cool for at least 15 minutes before drizzling with caramel and sprinkling with salt.

For the dulce de leche caramel drizzle: Because dulce de leche doesn’t “set” like frosting, it’s best to drizzle the pretzels right before serving. Place them in an airtight container to keep them fresh until you are ready to serve. When ready to serve, put the dulce de leche into a heatproof bowl and microwave it for 30-60 seconds until slightly thin. Then place it in a zip bag and seal the bag. Cut a small hole in the corner of the bag and “pipe” the warm caramel over the soft pretzels. Sprinkle with coarse sea salt and serve.

Prep 40 minute(s) active time. Makes 8 large or 16 minis.