In a food processor, pulse together flour, thyme, and 1/4 teaspoon salt. Pulse in butter until mixture is crumbly, then pour water in through the tube, 1 tablespoon at a time, and pulse until a cohesive dough forms.
Press dough into a tart pan, trim edges, and put into the freezer.
Wash carrots and cut long strips using a vegetable peeler. They do not need to be evenly sized; irregularity will make the carrots look more rose-like.
In a small bowl mix together cheese, chives, parsley, 1/2 teaspoon salt, and pepper.
Remove tart from the freezer and spread cheese mixture into the crust.
To form the carrot roses, roll up a strip of carrot, then roll another strip around it. Continue until you have the desired size, then gently press carrot rose into the cheese so it retains shape.
Continue until tart is filled.
Drizzle olive oil over the top of the tart and bake for 25-30 minutes.