Place flour, sugar, and yeast in the bowl of a standing mixer and mix until combined. Stir in Salt. Attach the dough hook to the mixer, then add water and oil and mix on low speed until dough comes together, 2-3 minutes. Continue mixing for another 8 minutes on low-medium speed until dough is soft and pulls away from the sides of the bowl.
Place dough in a large bowl brushed with oil, and toss to coat (the fat will keep the dough from drying out). Cover with plastic wrap and let sit in a warm place or on the counter for 1-2 hours, or until doubled in size. Keep in mind that rising will be slower in cold weather.
When the dough has risen, gently punch it to remove air. Divide the dough into 15 equal portions (each weighing about 45 grams) and shape each one into a strip about 20cm long. Gently stretch each strip and tie into a simple knot. Arrange knots on a baking sheet lined with parchment paper, keeping as much space between them as possible. Cover and let rest for 45-60 minutes or until again doubled in size.
Meanwhile, set the oven rack to the middle position and preheat to 350°F/180°C.
Melt 1 tablespoon butter in a small skillet over medium heat. Add garlic and cook for 2-3 minutes, until fragrant and color deepens slightly. Stir in the rest of the butter until melted, then add basil and salt and turn off the heat.
Right before baking the knots, spread them with half of the butter-garlic mixture. Bake for 15 minutes. Take the pan out and spread knots with the remaining butter mixture. Bake for an additional 5 minutes until golden brown. Allow pan to cool on a wire rack for 5 minutes. Transfer knots to a wire rack to cool completely.
Serve warm or at room temperature.
Knots are best the same day they are made, but can be frozen for up to 2 months.