To make the filling:
Combine garlic, olive oil, goat cheese and thyme in a small bowl. Mix until smooth, and season with salt and pepper.
For the blossoms:
In a bowl, whisk together beer and egg. Whisk in 1 cup of the flour and continue adding extra flour, 1 tablesppon at a time, until mixture has the consistency of thin pancake batter, Whisk in butter and season to taste with salt, pepper. Let rest 10 minutes.
Meanwhile, in a deep heavy pot fitted with with a deep-frying thermometer, heat 1 inch of oil to 375°. Stuff each blossom with a few tablespoons of the goat cheese mixture, and press petals closed.
Working quickly, in small batches, dip filled blossoms into batter, coating each completely; and fry, turning once, for 1 1/2 to 2 minutes, or until golden and crisp. Use slotted spoon to transfer blossoms onto paper towels to drain. Make sure the oil returns to 375° before adding each new batch of blossoms.
Sprinkle fried blossoms with salt and serve immediately.