Cut the baguette on a diagonal into 1/2 to 3/4 of an inch slices (makes about 22 slices). Arrange into one layer on a baking sheet. Place under a broiler set to high until the top of the bread is lightly toasted.
Add the feta, yogurt, garlic, and 1 tablespoon of basil to a small bowl and mash together with a fork. Store covered in the refrigerator for up to 8 hours.
In a small bowl, add the olive oil, vinegar, oregano, salt, and pepper. Whisk until well combined. Add the tomatoes, cucumber, red onion, and remaining basil. Stir to combine. Store covered in the refrigerator for up to 8 hours.
Divide the feta mixture between the bread slices. Spread into a thin layer on the toasted side of the bread. Top with the tomato mixture.
Slice the bread, and prepare the feta and tomato mixtures ahead of time for a quick assembly before serving.