For the chips, peel the potatoes and cut into about 1cm/½in square chips by 7cm/3in long - the most important thing is that the chips are more or less all the same size to ensure they cook evenly. Rinse the chips in cold water to remove excess starch and dry thoroughly on kitchen towels.
Fill a deep-fat fryer or a large, deep, heavy-bottomed pan two-thirds full with vegetable oil. Heat the oil to 140C-160C/285F-300F (use a probe thermometer to check the temperature if you're not using a deep-fat fryer). (CAUTION: Hot oil can be dangerous. Don't leave unattended)
Carefully place the chips in the hot oil and cook for about eight minutes or until just cooked through. Remove from the oil using a slotted spoon and drain on kitchen paper. Retain the oil in the pan and turn the heat up slightly to increase the temperature of the oil to 160-180C/320-355F.
For the steak, heat a ridged grill pan until hot. Brush the steaks with some of the vegetable oil. Season on both sides with salt and freshly ground black pepper. Place the steaks on the hot grill pan. After a few minutes, turn the steaks 90 degrees in the pan, to give diamond-patterned grill marks.
Turn the steaks over and repeat on the other side until they're cooked to your liking. For rare steaks, brown them on both sides as described and cook for an additional minute. For medium rare, cook for an additional 2-3 minutes or 4-5 minutes for well done - although exact cooking times will depend on the thickness of the steaks.
Remove the steaks from the pan and allow them to rest while you cook the chips a second time.
Check the temperature of the oil for the chips - it should be between 160C-180C/320F-355F. Add the cooked chips to the oil and fry for 2-3 minutes or until crisp and golden. Remove from the hot oil using a slotted spoon and drain on kitchen paper.
Serve the steaks and chips with grilled tomatoes and mustard on the side.