Place the roughly chopped onion in a small food processor and blend until very finely minced.
Transfer the onion to a small saucepan and cook over low heat, stirring regularly, until most of its natural moisture has evaporated. Do not let the onion brown.
Meanwhile, combine the garlic clove and 25 ml of olive oil in a tall measuring jug. Blend briefly with an immersion blender until the garlic is finely incorporated into the oil.
When most of the liquid has evaporated from the onion, add the garlic oil. Increase the heat slightly and cook for approximately 2–3 minutes, stirring frequently.
Add a small pinch of sugar and sea salt. Blend the ripe tomatoes until finely chopped or puréed, then stir them into the onion mixture.
Cook the sofrito gently over low heat for approximately 30–40 minutes, stirring regularly, until it becomes deep red, thick and highly concentrated. Measure out 4 tablespoons for the paella and reserve any remaining sofrito.
To make the garlic-parsley oil, combine the extra virgin olive oil, fresh parsley, garlic and a small pinch of sea salt in a mini food processor or tall measuring jug. Blend until you have a fine, fragrant green oil. Measure out 2 teaspoons for the paella. Refrigerate or freeze any unused oil promptly.
Pour the chicken stock into a small saucepan and heat until almost boiling. Add the Carmencita paella seasoning, saffron threads and finely chopped rosemary. Stir well and allow the flavors to infuse for approximately 10 minutes. Keep the stock hot while preparing the chicken. Taste and add salt only if needed.
If using boneless chicken thighs, cut them into generous bite-sized pieces. If using bone-in chicken, choose small pieces that can cook through within the paella's total cooking time; larger bone-in pieces should be partially cooked before the rice is added. Season the chicken lightly with sea salt.
Heat the 4 tablespoons of mild olive oil in a 30 cm (12-inch) paella pan over medium-high heat. Add the chicken and brown well on all sides. The chicken does not need to be fully cooked at this stage, but it should develop a lovely golden surface.
Reduce the heat slightly. Add 4 tablespoons of homemade sofrito and 2 teaspoons of garlic-parsley oil. Stir for approximately 2 minutes, coating the chicken with the concentrated tomato and herb mixture.
Sprinkle the paella rice evenly into the pan. Gently stir for approximately 1 minute, allowing the grains to become coated in the sofrito and oil.
Pour the hot saffron-infused chicken stock evenly over the rice. Use your spoon just once to distribute the grains in a thin, even layer across the bottom of the pan.
From this point onward, do not stir the rice.
Let the paella cook at a lively simmer over medium-high heat for approximately 7–8 minutes. Then reduce the heat to medium-low and continue cooking for another 8–10 minutes. Adjust the heat to maintain an even simmer across the pan.
During the final 5 minutes of cooking, scatter the peas evenly over the rice. Do not stir them in.
Check the rice toward the end of cooking. If the liquid has evaporated but the grains are still too firm, add a small splash of hot chicken stock or hot water around the edges of the pan. Continue cooking without stirring. Make sure the chicken is completely cooked through, reaching at least 74°C (165°F) in its thickest part.
When the rice is nearly tender and the liquid has been absorbed, increase the heat slightly for approximately 30–60 seconds to encourage the formation of the socarrat, the thin toasted layer of rice at the bottom of the pan.
Listen for a gentle crackling sound and pay attention to the aroma. As soon as you notice a pleasantly toasted, nutty smell, remove the pan from the heat. Do not let the rice burn.
Cover the pan loosely with aluminum foil or a clean kitchen towel and allow the paella to rest for approximately 5 minutes.
Scatter over a little finely chopped parsley if desired and arrange the lemon wedges around the edge of the pan.
Bring the paella pan directly to the table and serve immediately, making sure everyone gets a little of the delicious toasted rice from the bottom.