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, dust each ball lightly with flour, and set them aside, covered, for 15 minutes.
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 roll each ball into a small disc, then lift the disc by its edges and stretch it gently with your fingers, while letting 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.
Make sure the grill is screaming hot. You can also use a grill pan on a stovetop, if you don't have a grill. Place the naan on the grill. You will immediately see it start to bubble up and turn opaque. Put down the grill cover or, if using a pan, cover with a lid. Let the naan grill for a minute, then, using tongs, carefully turn it by 90 degrees to get those lovely cross-hatch grill marks. Grill another minute, then flip and repeat for the other side. Altogether, you should need no more than 3 minutes on the grill for each naan, possibly less.
As soon as you take the naan off the griddle, brush it with melted vegan butter or olive oil. Keep your naans wrapped in a kitchen towel until ready to serve.
You can reheat any leftover naans on the griddle before serving.