Heat oven to 400 degrees Fahrenheit. Line two baking sheets with parchment paper.
Stir together the flour, cheese and 1 teaspoon salt in a large bowl, using a fork. Pour in the cream and stir with a flexible spatula until no loose flour remains. Dump the dough onto a floured work surface. With floured hands, pat the dough into a rectangle. Using a rolling pin, roll the dough into a 12"x17" rectangle, between 1/8 and 1/4 inch thick, with a long side facing you. Reflour your work surface and move the dough around as you roll to keep it from sticking.
Trim the rectangle to about 10 1/2" x 15". Using a pizza cutter or sharp knife, thinly slice the dough lengthwise into 1/4 inch strips. Reroll and slice the scraps. Place 16 - 18 strips on each prepared baking sheet, leaving 1/2 inch between each one. Lightly brush cheese sticks with butter olive oil and sprinkle lightly with coarse sea salt.
Bake for 12 minutes, rotating the baking sheets at the halfway point, until the sticks are lightly browned. Let cool and serve. Store in airtight container at room temperature.