Preheat your oven to 400°F. Line a sheet pan with aluminum foil or parchment paper. Arrange the tomatoes in a single layer, add 1 tablespoon of the olive oil, and mix well to coat the tomatoes. Roast for 20 minutes, then set aside to cool.
While the tomatoes roast, toast your almonds. Add them to a small skillet over medium-low heat and cook, tossing occasionally until golden brown for about 5 minutes.
Add the toasted almonds and the garlic to a food processor and pulse until finely ground. Now that your tomatoes are cooled, place them in a bowl, draining as much water out of them as possible. Add the cooled roasted tomatoes, Sangiovese, basil, Parmesan, and salt to the food processor and pulse well to combine, using a spatula on the sides of the food processor to push any food off of the sides. While the processor is running, drizzle the olive oil through the shoot until the mixture is emulsified and smooth.