Place the yeast in a large bowl or the bowl of a stand mixer. Add the sugar, nondairy milk, and ½ cup water. Let the yeast stand at least five minutes until it starts to look frothy and "blooms"
Add the flour and salt to the bowl and begin to knead, slowly drizzling in additional water until your dough comes together in a ball that's just slightly sticky (traces of the dough will stick to your fingers when you touch it). Keep in mind that you may not need all of the water, so don't dump it all in at one go.
Drizzle the oil on top of the dough, turn it over once or twice to make sure the oil coats the dough, cover the bowl tightly with cling wrap or a lid or a kitchen towel, and set it aside to rise in a warm place for an hour to 90 minutes.
After the dough has risen, turn it out on your work surface. Knead it lightly, form into a disc and cut into eight even pieces, the way you would a pizza. Roll each piece into a ball (it won't be firm), dust each ball lightly with flour, and set them aside, covered, for 15 minutes.
Meanwhile, make your garlic butter mixture by heating the butter in a small saucepan along with the garlic. Let the butter and garlic cook together for 3-4 minutes over medium-low heat until the garlic flavor infuses the butter and the garlic starts to turn a light golden. You don't want the garlic to burn. At this point, turn off the heat and stir the herbs into the melted vegan butter. Set aside.
To shape the naan, either roll each ball into a teardrop shape or a round with a rolling pin. You can dust your work surface lightly with flour if needed. Or use your fingers to shape each ball into a small disc, then lift the disc by its edge and let the dough stretch and fall with the aid of gravity. Continue shaping by moving your fingers along the edges. If you're not used to doing this, it's possible your dough could tear, so be careful. If you do get a tear, patch it up by pressing the dough together and continue shaping with a rolling pin.
Heat a cast iron skillet or any griddle over high heat until it's screaming hot. Place the naan on it. You will immediately see it start to bubble up and turn opaque. Once the underside gets golden-brown spots, turn over and continue cooking the other side. This process should take you no more than two minutes or less on either side.
As soon as you take the naan off the griddle, brush it with the garlic-herb-butter mixture on one side. Keep your naans wrapped in a kitchen towel until ready to serve.
You can reheat any leftover naans on the griddle before serving.