Make the cheese puffs: Position racks in the upper and lower thirds of the oven and preheat to 400 degrees F. Line 2 baking sheets with parchment paper. Bring 1 1/4 cups water, the butter and 1 teaspoon salt to a simmer in a medium heavy-bottomed saucepan over medium heat, stirring until the butter melts. Add the flour all at once and stir vigorously with a wooden spoon until the mixture pulls away from the sides of the pan and forms a ball. Continue cooking, stirring vigorously, until the dough is no longer sticky, 1 to 2 more minutes. Remove from the heat and let cool 2 to 3 minutes.
Transfer the dough to a stand mixer fitted with the paddle attachment; beat in the eggs one at a time on medium-high speed until the dough is smooth. Add the celery salt and a few grinds of pepper and beat 1 more minute. (The dough should be tight and stiff.) Beat in the gruyere.
Transfer the dough to a large pastry bag fitted with a 1/2-inch round tip. Pipe 1 1/2-inch mounds of dough 2 inches apart onto the prepared baking sheets (about 18 per sheet). Smooth the tops of the dough mounds with a damp finger. Transfer to the oven and bake until puffed and golden, about 30 minutes, switching the position of the pans halfway through. Turn off the oven. Remove the baking sheets and use a needle or toothpick to poke a hole in each puff to release steam. Return to the oven until crisp, about 20 more minutes. Remove from the oven and let the puffs cool completely on the baking sheets.
Meanwhile, make the cheese spread: Beat the cream cheese, goat cheese, garlic, parmesan and herbs with a mixer until smooth. Season with salt and pepper. Clean out the pastry bag and fill with the cheese spread.
Assemble the tower: Arrange a 7-inch circle of cheese puffs on a platter, using the cheese spread to secure them to the platter. Fill the base circle with more puffs for stability, then continue building a cone-shaped tower of smaller circles, using the cheese spread to attach the puffs. Garnish with thyme sprigs and parmesan. The tower will keep at room temperature for up to 1 hour.