Rinse rice in a strainer until the water runs clear.
In a large sauté pan over medium high heat, add 3 tablespoons of oil olive. After a few minutes, add fennel and onions sauté until soft but not colored. Add the garlic and Piment d' Espelette, continue to sauté for another 2 minutes, and then add tomatoes. Sauté for another 2 minutes. Add the rice and stir to combine.
Pour in the vermouth, bring to a boil and reduce liquid by half. Add chicken broth and bring to a boil. Reduce heat to low and simmer until rice is tender and the liquid is absorbed about 20 minutes.
About 10 minutes before rice is done, in a large sauté pan over medium-high heat add the remaining 3 tablespoons of olive oil. After a few minutes, add the shrimp and sauté until pink and cooked through on both sides (you may need to do this in two batches). Season with salt and pepper.
Gently mix the herbs into the rice. To serve, spoon rice on to a large platter, arrange the shrimp over the rice and sprinkle with the crumbled feta cheese. Add lemon wedges to squeeze lemon juice over the rice and shrimp.