In my area, restaurants that mainly serve shoyu (soy sauce), ramen and tonkotsu (pork bone broth) ramen areis common, and miso ramen specialty restaurants are rare.

A Ramen Restaurant Specializeding in Miso Flavour

I went to a ramen restaurant which specialized in miso flavorured ramen with my family.

In my area, restaurants that maicommonly serve shoyu (soy sauce) ramen and tonkotsu (pork bone broth) ramen are common, and mit iso ramen specialty restaurants are to find a restaurant specializing in miso flavoured raremen.

At that restaurant, you can eat ramen usingare served miso from various regions.

Add more detail of where is it from and give a few examples of what they serve

I ordered thatsomething called “Hokkaido miso ramen.” ¶
Normally, when I think of Hokkaido ramen, I think of whiterecollect a white colour miso soup, but this time itI was served red miso.

It was a little different than usual, but it was delicious.

A Ramen Restaurant Specialized In Miso Flavor

You need a preposition to connect the relationship between the restaurant and the speciality of the restaurant.

You can say "A Ramen Restaurant That Specializes in Miso". In English, it will be more common to just hear "miso" -- we are not familiar with the phrase "miso flavor" since we are mostly only familiar with "miso soup".

I went to a ramen restaurant specialized in miso flavor with my family.

Same as above. Or, "I went to a ramen restaurant that specializes in miso flavor with my family." Your grammar is also acceptable, this is only an alternative.

A Ramen Restaurant Specializeding in Miso Flavor/Taste

"Specialize" connects with "in."

I went to a ramen restaurant specializeding in miso flavor with my family.

At thatBut at this restaurant, you can eat ramen using miso from various regions.

"At that restaurant" confuses which restaurant of the three we are talking about. Even more specific would be "but at this miso restaurant," or "but at this new restaurant," et cetera.

I ordered thatone called “Hokkaido miso ramen.” ¶
Normally, when I think of Hokkaido ramen, I think of white miso soup, but this time it was red miso.

"That" is actually okay here, but is a very old-fashioned tone.

It was a little different than usual, but it was delicious.

You can also write, "It was a little different than usual, but (still) delicious."

I went to a ramen restaurant that specialized in miso flavor with my family.

I ordered one that's called “Hokkaido miso ramen.” ¶
Normally, when I think of Hokkaido ramen, I think of white miso soup, but this time it was red miso.