Begin by making a roux, which will keep the dough moist and chewy. To make the roux, add 1/3 cup bread flour in a saucepan with 1/2 cup nut milk and 1/2 cup water. Heat over medium heat, whisking constantly until smooth. Continue whisking until a thick paste forms; it should be similar to the consistency of mashed potatoes. Remove roux from heat and scrape into a large mixing bowl.
In a separate small bowl, heat 2 tbsp of nut milk for 15-30 seconds in the microwave. Add yeast and whisk until frothy. Let sit for 5 minutes.
Meanwhile, add sour cream, sugar, salt, 6 tbsp aquafaba, 4 tbsp butter (cut in cubes), and 5 cups of bread flour to mixing bowl with roux. Add yeast and mix on low speed using a stand mixer fitted with a dough hook.
Slowly increase speed of mixer until a smooth dough forms. Place dough onto a nonstick surface and knead lightly before forming into a ball. Place into a large bowl and cover with plastic wrap. Let the dough rise for at least 1-1.5 hours, or overnight if prepping ahead.
Once dough has doubled in size, remove from bowl and place onto a floured surface. Separately, coat an oven-safe dish with 2 tbsp butter and set aside.
Knead dough thoroughly, removing air bubbles. Then roll out dough and stretch into a square shape. Sprinkle chopped chives evenly over the dough.
Loosely roll dough from one end to the other, flattening into a long rectangle.
Roll out the rectangular-shaped dough to flatten further. Using a pizza wheel or dough cutter, cut dough into 2-3" square pieces. Pinch any loose edges.
To create the bread roll shape, place dough square beneath your palm and roll quickly in a circular motion until a tight ball is formed.
Place bread roll balls into the buttered oven-safe dish and cover with plastic wrap. Set aside and let rise for 45-60 minutes.
When dough is ready, preheat oven to 375 degrees, placing the oven rack towards the center of the oven. Brush remaining 3 tbsp aquafaba over top of rolls before placing in the oven.
Bake approx. 25-30 minutes. When there are about 3 minutes left, brush tops of rolls with melted butter. Sprinkle with salt or chives, if desired.
Let cool in oven-safe dish before removing and serving.