Recipe(tried): Rio City Sourdough Cheese Bread (copycat recipe)

We ate at the Rio City Cafe, Sacramento, CA after a voyage up the Sacramento River from Isleton in our 27' Bayliner for Mother's Day. What an unexpected treat!
The sourdough cheese loaf was an immediate hit with all of us. Here's my best facsimile:

RIO CITY SOURDOUGH CHEESE BREAD
(copycat recipe)

1 sourdough round
2 slices (1x3-inches?) Gruyere cheese
2 slices (1x3-inches?) Swiss cheese
2 slices (1x3-inches?) or shredded Parmesan cheese
1/3 cup olive oil
2 tbsp butter
3 tbsp balsamic vinegar
1/4 tsp chives flakes
1/2 tsp minced garlic
Red pepper flakes, to taste
Salt and pepper, to taste

Slice loaf across top in a "tic-tac-toe" fashion, leaving bottom crust uncut.

Spread butter into slices and on bottom underside of crust.

Arrange cheeses as desired inside cuts

Lightly sprinkle a portion of chives and red pepper flakes into cuts.

Bake at 325 degrees F for 12-15 minutes.

Using a plate with a raised rim to hold fluids, combine oil and balsamic vinegar, salt and pepper, red pepper flakes and garlic. Set loaf into mixture and serve.