In the bowl of a stand mixer, using the paddle attachment, combine 2 cups flour, yeast, sugar, and salt.
Add warm water and oil to flour mixture. Blend at low speed until moistened. Beat 4 minutes at medium speed.
Switch to the dough hook and mix in the remaining flour a little at a time, to make a soft dough, add more or less flour as needed. Knead the dough for 5 minutes until smooth and elastic. Place dough in lightly oiled bowl and turn to grease top. Cover; let rise in warm place until double about 30 minutes.
While dough is rising, make cream cheese dip: In a large mixing bowl, beat cream cheese and sugar until smooth. Stir in strawberry jam and refrigerate until ready to serve.
Preheat oven to 450°F. In a 3-quart saucepan, bring 8 cups water and 1/3 cup baking soda to a simmer.
Turn dough onto lightly floured surface; punch down to remove air bubbles. Divide dough into 8 pieces. Roll each piece into a 20-inch long rope. Cut each rope in half to make 16 pretzel sticks. Place on greased or silicone-lined cookie sheet.
Add pretzels, four at a time, to the simmering water and cook 10 seconds on each side. Remove with slotted spoon. Place on prepared cookie sheet.
Beat egg in a small bowl with 1 teaspoon water. Brush egg wash on one side of the pretzel sticks. Sprinkle a thin layer of coarse sugar on top.
Bake for 10 minutes until deep golden brown.
Best when served the same day.