To make pretzels: Combine warmed water, sugar, yeast, and butter in bowl of a stand mixer and mix with a dough hook just until combined. Let sit for 5 minutes.
Add salt and 4 1/2 cups flour to the mixture and blend on low speed until combined. Increase the speed to medium and continue kneading until the dough is smooth and begins to pull away from the side of the bowl, about 3 to 4 minutes. If the dough appears too wet, add additional flour, 1 tablespoon at a time. Remove dough from bowl, turning out onto a flat surface and knead into a ball with your hands.
Coat a large bowl with canola oil, add the dough and turn to coat with the oil. Cover with a clean towel or plastic wrap and place in a warm spot until the dough doubles in size, about 1 hour.
Preheat the oven to 425 degrees F.
Bring 3 quarts of water to a boil in a large pot.
Remove dough from bowl and place on a flat surface. Divide the dough into 8 equal pieces. Roll each piece into a long rope. To shape into pretzels, take the right side and cross over to the left. Cross right to left again and flip up. Slowly add the baking soda to the boiling water. Boil the pretzels in the water solution, 2 at a time for 30 seconds, splashing the tops with the warmed water using a spoon. Remove with a large flat slotted spatula. Place pretzels on parchment lined baking sheet, brushing the tops with beaten egg. Sprinkle coarse salt on pretzel and then bake for 15 to 18 minutes until golden brown. Remove from oven and let cool until ready to serve.