Preheat the oven to 180C/350F/Gas 4. Lightly oil a 39x35cm/15¼x13¾in baking tray and line with baking parchment.
Scatter the Brazil nuts over a baking tray and place in the oven for 10 minutes, or until slightly roasted and a light golden-brown. Set aside to cool.
Place the sugar, butter, cream of tartar and 50ml/2fl oz water in a deep, heavy-bottomed pan over a very low heat, stirring until the sugar has dissolved. To check the sugar is completely dissolved, dip the back of a metal spoon into the mixture; if you can see any sugar crystals on the spoon it needs a few more minutes.
Put the sugar thermometer in the pan and bring the mixture up to the boil, without stirring. Carefully let it bubble until the thermometer reaches 130C/266F. (CAUTION: boiling sugar is extremely hot. Handle very carefully. Use a deep pan to avoid bubbling over.)
Remove the pan from the heat and let it sit for a minute. Using a fork and a spoon, carefully dip each Brazil nut into the hot toffee. Alternatively, add a handful of Brazil nuts at a time and stir to coat before removing them individually. Take care when handling the toffee as it will be very hot. If the toffee starts to harden in the pan, briefly return it to the heat.
Place the toffee-coated Brazils on the baking tray and drizzle over any toffee left in the pan. Leave for an hour to cool and set.
Store in a cool, dry cupboard and they will last for five days or so.