Combine flour, sugar, yeast, and salt in bowl of electric mixer fitted with dough hook.
Add sourdough starter, eggs, oil, and water.
Mix on low speed until combined.
Increase speed to medium-high.
Knead dough for 8-10 minutes, until smooth.
Place dough in dough rising bucket that has been sprayed with cooking spray and put the lid on.
Allow to rise in a warm place until doubled in bulk, about 1 hour.
Turn dough out and use a bench knife and digital scale to divide into 2½ ounce pieces.
Roll each piece into a ball and place seam side down in bun pan that has been sprayed with non stick cooking spray. (If you don't have a bun pan, a rimmed sheet pan will work fine.)
Brush tops with olive oil and cover with plastic wrap.
Allow to rise until doubled in bulk, about 1 hour.
While dough is rising, heat oven to 400℉/200℃.
Bake until golden brown, 15 to 20 minutes.