Mix milk and water in a pot over low heat. Heat, stirring constantly, until an instant-read thermometer inserted into the pot reads 110 degrees F (43 degrees C). Remove from heat. Add sugar and stir to dissolve. Pour mixture into a cup or other cylindrical glass; sprinkle yeast on top. Let mixture rest until yeast is frothy and fragrant, about 10 minutes.
Stir flour and salt together in a large mixing bowl. Pour in yeast mixture and mix until a sticky dough forms.
Turn dough out on a floured work surface and knead quickly for 5 minutes. Shape dough into a ball. Grease a large bowl with 1 tablespoon olive oil. Add dough; toss around the bowl a few times to coat evenly with oil. Cover with plastic wrap and a towel. Let rise in a warm place until doubled in size, about 1 hour.
Return dough back to the work surface and punch down. Coat your hands with a little olive oil and knead again for 1 minute. Divide into 5 balls. Flatten balls out into thick rectangles. Place rectangles of dough onto a greased baking sheet. Brush tops with a thin coat of olive oil. Let rest for 20 minutes.
Preheat the oven to 350 degrees F (175 degrees C) while dough rests.
Bake bread in the preheated oven for 12 minutes. Switch to the broil setting until the tops of rolls turn golden brown, about 1 minute. Remove from the baking sheet and allow to cool completely. Cut rolls in half lengthwise.