Preheat a cast-iron griddle or skillet over medium-high heat until hot. Add the shishito peppers and cook, flipping as needed, until blistered and browned, about 5 minutes. Meanwhile, add the lime cut-side down and cook until charred.
In a bowl, toss the broccolini with a drizzle of olive oil and a sprinkle of kosher salt and pepper. Add the broccolini to the griddle and cook until charred and the stems are fork-tender, about 7 minutes.
Meanwhile, reserve a handful of the peppers for serving, and remove the stems from the remaining peppers.
To the carafe of a food processor, add the stemmed peppers, hazelnuts, peas, cilantro and white balsamic vinegar, and season with salt and pepper. Pulse until coarse, then, with the food processor running, slowly add 1/2 cup olive oil and blend until smooth. Taste and adjust the seasoning.
To serve, spread the romesco sauce in a shallow bowl or platter. Top with the charred vegetables, sliced jalapenos and a drizzle of olive oil. Sprinkle with the flaky salt and a handful of cilantro leaves. Squeeze the charred lime over the top just before serving.