Lightly grease a bowl. Set it aside.
In a small saucepan, warm 3/4 cup of the milk and 1/4 cup of the butter over low heat until warm.
Pour the warm milk mixture into the bowl of a stand mixer fitted with a dough hook attachment.
Add in 1 cup of the flour, 3 tablespoons of the white sugar, 1/2 teaspoon of the salt, the yeast, 1 teaspoon of the maple extract, and the egg.
Beat the flour mixture on low for 2 minutes.
While continuing to beat, gradually add the remaining 1 3/4 cups of the flour. Beat on medium speed until a soft dough forms. Add the extra flour, a little at a time, if the dough doesn't appear to be coming together.
Increase the speed to medium-high and beat until the dough is soft and supple, for about 6 minutes.
Using the extra flour, lightly dust a work surface. Transfer the dough to the prepared work surface.
Knead the dough with your hand until it is smooth and elastic, about 1 minute.
Form the dough into a ball. Place the dough ball in the prepared bowl. Cover the dough loosely and let it sit in a warm place until it doubles in size, about 45 minutes-1-1/2 hours.
Prepare two baking sheets by layering a cooling rack on top of a baking sheet and lining them with parchment paper.
In a small bowl, combine 1/4 cup of the melted butter with the remaining white sugar, the pecans, the cinnamon, and 1 teaspoon of the maple extract.
Once the dough has risen, divide it into 2 equal pieces. Roll each piece into a 12-inch circle.
Place the first circle on the prepared sheet pan. Top the first circle with 1/2 of the filling mixture, spreading it as thin as possible.
In the center of the dough round, mark a circle about 2 inches in diameter. Using kitchen shears or a knife, cut from the outer edge of the dough to the edge of the center mark, making 10-12 wedges.
Gently lift and twist each wedge a few times, tucking in the end so it stays twisted.
Repeat the rolling, filling, and twisting process with the remaining dough and filling mixture.
Lightly cover the pastries with plastic wrap. Let the dough rise for 45 minutes-1 hour.
Preheat the oven to 350 degrees F.
Bake until the top is lightly golden-brown, for about 18-22 minutes.
Transfer the twists from the oven and let them cool for 5 minutes.
In a bowl, whisk the powdered sugar, the remaining melted butter, 1 tablespoon of the remaining milk, the remaining maple extract, and the vanilla extract together into a glaze. Add the extra milk, a little at a time, if the glaze is too thick.
Drizzle the glaze over the twists.
Serve!