Heat a frying pan over medium heat, add the almonds and lightly toast, constantly tossing for an even colour. Cool, then pound to coarse crumbs using a mortar and pestle (or if you want to speed up the process, blitz in a small food processor). Tip into a bowl, bruise the basil leaves with a little salt using the mortar and pestle. Return the ground almonds to the mortar, add the parmesan and pound to form a rough paste. Transfer to a large bowl and set aside.
In the same pan used to toast the almonds, heat the oil (reserving 1 tablespoon) over medium-low heat. Add the garlic and anchovies and cook for 2-3 minutes, or until the garlic just begins to change colour. Stir in the tomatoes, season with salt and pepper and cook for 2 minutes until the tomatoes, are just warmed through and beginning to blister a little. Remove from the heat, allow to cool slightly, then add basil and ground almonds.
Season the chicken on both sides with salt and pepper. Wipe the pan clean and place back on the heat, add the remaining oil and, when hot, add the chicken, skin-side down. Cook over medium-high heat for 3-4 minutes until the skin is golden and really crispy. Turn the chicken, add the speck and cook the chicken for another 3-4 minutes until golden, then remove from the pan. Set aside and rest for 3 minutes.