Bring on the bagel, but say goodbye to the fatty cream cheese; a schmear of yogurt spread serves as a satisfying substitute.
Line a sieve with three layers of cheesecloth and set over a bowl. Place yogurt in center of cheesecloth; gather the corners, twisting to tighten the cloth around the yogurt; and tie with twine. Transfer to the refrigerator for at least 24 hours and up to three days.
Remove yogurt cheese from cheesecloth and transfer to a medium bowl. Stir in salt, pepper, and basil.
To build sandwiches, spread cheese onto cut sides of bagels. Top with tomato, red onion, baby arugula, and a drizzle of extra virgin olive oil. Close sandwiches and wrap in parchment paper or plastic wrap until ready to eat.