Preheat the oven to 400° F.
Place the peppers in a large baking dish with the rounded side facing down and rub with 2 tbsp olive oil plus a pinch of salt. Roast for 30-40 minutes, until tender and beggining to char.
Meanwhile, make the rice. Heat a large lidded pot over medium heat and add the remaining 2 tbsp of olive oil. When shimmering, add the shallot and sauté for about 10 minutes, until just begining to caramelize.
Add garlic, thyme, rosemary, sundried tomatoes and rice. Cook for 5 more minutes before adding the wine to deglaze the pan. Allow the wine to absorb for a few minutes, then add the stock, chickpeas and salt.
Bring to a boil, then reduce the heat to low and cover. Cook for 15-20 minutes, stirring ocassionally. If the rice seems dry, add another 1/2 cup of warm stock.
To make the pesto, add all ingredients to a high speed blender or food processor. Blend until combined, scraping down the sides as needed. If the pesto seems to thick, add another tbsp of olive oil. Taste for salt and add more as needed.
To assemble the peppers, spoon about a cup of rice into each and top with the sunflower basil pesto. Serve fresh.