Combine feta cheese, yogurt and 1 Tbsp. olive oil in a food processor. Process until smooth. Set aside.
In a bowl, whisk together the vinegar, mustard and oregano. Whisking, slowly pour in the remaining 3 Tbsp. olive oil until incorporated. Remove seeds from tomatoes and cut into cubes. Toss tomatoes with the vinaigrette and set aside.
Heat a grill to 400 degrees. Cut the onion into large chunks and brush with olive oil. Place directly onto the grill grates, flipping when the onion begins to char. Grill about 10 minutes until very soft and pliable. Slice into smaller pieces. Season with salt and pepper.
Slice the baguette and brush one side with olive oil. Grill, oiled side down, until toasted, about 3-4 minutes. Remove the toasts. Top with whipped feta, grilled onion and tomatoes.