DUMP THE ZUCCHINI IN A SINK FULL OF WATER AND LEAVE THEM THERE FOR 15 MINUTES. USE A VEGETABLE BRUSH TO REMOVE ANY SAND OR GRIT FROM THE OUTSIDE.
TRIM THE ENDS. SLICE THE ZUCCHINI LENGTHWISE IN HALF, THEN IN QUARTERS. CUT CROSSWISE INTO 2-INCH PIECES.
TOSS IN A COLANDER WITH SEVERAL TABLESPOONS OF SALT AND ALLOW TO SIT FOR AT LEAST 15 MINUTES. THE SALT WILL DRAW OUT SOME OF THE MOISTURE. RINSE OFF THE SALT. TOSS IN THE COLANDER, THEN LAY OUT ON A KITCHEN TOWEL AND ROLL GENTLY TO DRY.
TRIM THE GARLIC CLOVES AND SLICE THINLY. RESERVE IN A SMALL BOWL.
SCORE THE SKIN ON THE SMOOTH END OF THE TOMATOES IN THE SHAPE OF AN X. HOLD A BOX GRATER INSIDE A BOWL AND HOLDING THE TOMATO SCORED SIDE OUT, GRATE THROUGH THE LARGEST HOLES IN THE GRATER. THIS WILL REMOVE THE PULP, LEAVING THE SKIN IN YOUR HAND TO DISCARD.
HEAT ABOUT A 1/3 CUP OF OLIVE OIL IN A FRYING PAN OVER A HIGH FLAME. ADD ALL THE ZUCCHINI AND SAUTÉ FOR ABOUT 3 MINUTES, SO THE PIECES ARE SLIGHTLY BROWNED. ADD THE GARLIC AND TOSS WITH THE SQUASH TILL YOU CAN JUST SMELL THE GARLIC,
STIR IN THE TOMATO PURÉE, REDUCE THE HEAT TO MEDIUM AND CONTINUE TO COOK, STIRRING FREQUENTLY, UNTIL THE LIQUID HAS THICKENED.
EMPTY INTO A SERVING. GARNISH WITH TORN BASIL AND MINT.
SERVES 4-6