Preheat the oven to 425 degrees F. Toss the cherry tomatoes with olive oil, balsamic vinegar, garlic, salt, and black pepper in a rimmed baking dish.
Roast the tomatoes for 18 to 22 minutes, stirring once, until softened and lightly caramelized. Let them cool for 5 minutes so their juices thicken slightly.
Arrange 24 baguette slices on a baking sheet and brush them with olive oil. Bake for 7 to 9 minutes, turning once, until crisp and golden around the edges.
Blend the cottage cheese, feta, lemon juice, lemon zest, and black pepper in a food processor for 1 to 2 minutes, scraping down the sides as needed, until completely smooth and airy.
Spread a generous spoonful of whipped cottage cheese over each crostini. Top with the roasted tomatoes and a small spoonful of their garlicky pan juices.
Finish the crostini with fresh basil and a light drizzle of balsamic glaze. Serve while the bread is crisp and the tomatoes are slightly warm.