First, make the pickled peaches. Put the peach slices in a bowl and set aside. Tip the remaining ingredients into a saucepan with 50ml water and bring to the boil, stirring until the sugar has dissolved. Remove from the heat and leave to cool for 10 mins. Pour the mixture over the peaches and leave to pickle for at least 30 mins, or up to a few hours.
Heat the oven to 200C/180C fan/gas 6. Put the almonds and fennel seeds on a baking tray, drizzle with the rapeseed oil, and sprinkle over the smoked paprika and a little salt. Toss to coat. Bake for 8 mins, or until toasted and slightly crisp.
Pull away any tough outer leaves from the fennel bulbs (you can keep these to use for stock). Trim the bases, and remove the stems and fronds (again, reserving these for stock, if you like). Slice the bulbs in half along their cores, then lay them, cut-side down, on a chopping board. Very finely slice each half into half-moons, then tip into a bowl and drizzle with the lemon juice. Meanwhile, drain the pickled peach slices.
Drain the radishes and combine with the fennel and a large pinch of salt. Leave to sit for a few minutes, then stir in the peaches, most of the cheese and half the herbs. Drizzle with the olive oil and scatter over the toasted almonds and fennel seeds. Garnish with the rest of the herbs, and a bit more cheese.