Preheat the oven to 375ºF (190ºC) and line a baking sheet with parchment paper.
Spread the sunflower seeds on the baking sheet in a single layer and bake in the preheated oven for 5-10 minutes. The seeds are toast when they turn a golden color and become fragrant. Remove from the oven and immediately transfer the seeds to a plate.
Increase the temperature of the oven to 400ºF (200ºC). Take ½ cup of the cherry tomatoes and slice them in half. Spread the whole tomatoes and the halves out on the pan. Bake in the oven for 30-25 minutes until the cherry tomatoes are blistering and begin to char in areas. Remove from the oven and let the tomatoes cool.
Once the tomatoes are cool enough to handle, set aside the halved tomatoes, you will use these as a garnish.
Now add the whole roasted tomatoes, toasted sunflower seeds, chickpeas capers, garlic, lemon juice, thyme, red pepper flakes, and salt to a food processor.
Pulse 7-10 times to combine and then process continuously. Pour ¼ cup of the chickpea cooking liquid or canned liquid (or water if you have neither) while processing. Add more liquid as needed until the mixture comes together but there is still some texture (if you like a smoother hummus, continue to process until desired texture is reached). Taste and re-season. Transfer to a serving dish and garnish with the roasted tomato halves, sunflower seeds, and red pepper flakes.