Make the dough: Add the eggs, water, vegetable oil, and vinegar into the bowl of a stand mixer fitted with a dough hook attachment. Mix on medium for 30 seconds to combine. Add the flour, baking powder, and salt. Mix on medium-high for 15 minutes until a sticky smooth dough is formed, and it starts pulling away from the sides.

Transfer the dough to a lightly oiled bowl. Cover with plastic wrap or a damp towel and let it rest for 1 hour at room temperature. 

While the dough rests, make the filling: Rinse the rice until the water runs clear, then add it to a small pot with salt. Cover with ⅓ cup of cold water, and bring to a boil. Reduce the heat to low, cover, and cook for 12 minutes until the rice is tender. Remove from the heat, and stir in the butter. Fluff with a fork while the butter melts. Set aside to cool

In a large mixing bowl, combine the cottage cheese, sugar and tapioca flour. Add the cooled rice and mix well. The mixture will be loose. Refrigerate until ready to use.

Once the dough has rested, preheat the oven to 400 degrees, and line 2 baking sheets with parchment paper.

Assemble the knishes: Cover a work surface with a clean thin cotton cloth or bedsheet. Sprinkle lightly with flour and place the dough onto the surface. Using a rolling pin, roll out the dough into a large circle. Once it gets too large for the rolling pin, begin to gently stretch the dough by hand until it measures 20 inches in diameter. To avoid tearing, rest the dough every once in a while between stretching.

Evenly place the filling in a ring shape along the edge of the circle. Rub 1 teaspoon of oil into the center of the dough, and press a finger into the middle, creating a small hole.

Roll the edge of the dough over the filling, encasing it. Continue rolling into the center until the dough is a long ring log shape. As you roll, the center of the dough will tear. Roll out the log so that the filled width is about 1-inch thick.

Use the heel of your hand to cut 3 inch long pieces from the log to create each knish portion. Once all the knishes are separated, twist each knish end closed to seal in the filling, and stand them up vertically on the baking sheets. Use your thumb to press down the top sealed end. 

Brush each knish lightly with oil and bake for 30-35 minutes, or until the knishes are golden brown and cooked through.