Sharpening the restaurant's knives with 包丁研ぎ

Vocabulary Explanation: Collocations for cooking

Konju drops by Hakumei and Mikochi’s new house with a housewarming gift of herbal tea. She talks with Mikochi for a bit.

コンジュ:: 「そういえばハクメイは？」; “Come to think of it, where's Hakumei?”
ミコチ:: 「料亭(りょうてい)の包丁研(ほうちょうと)ぎに行(い)ってるわ」; “She's out sharpening knives for a restaurant.”; Literal: “She has gone to a ryōtei's knife sharpening.”

Key Points

1包丁研(ほうちょうと)ぎ = knife sharpening

研(と)ぐ is the verb for sharpening a blade on a whetstone, and 包丁(ほうちょう)を研(と)ぐ is the usual way to say “sharpen a kitchen knife”. The panel shows Hakumei with her knife and whetstone.
Put a noun before a verb stem and the pair becomes one compound noun with no を: 包丁(ほうちょう)を研(と)ぐ becomes 包丁研(ほうちょうと)ぎ, the same way 皿(さら)を洗(あら)う becomes 皿洗(さらあら)い, dishwashing. The compound can name the work, the tool, or the person who does it. Here it’s the work.
The same 研(と)ぐ goes with rice: 米(こめ)を研(と)ぐ means to wash rice by rubbing the grains together in water. Learn each use with its noun.

2料亭(りょうてい)の

A 料亭(りょうてい) is a traditional, high-end Japanese restaurant. の ties the job to that restaurant, so the knives belong to its kitchen.

3〜に行(い)ってる = has gone to do ~

に行(い)く after an action noun or verb stem gives the reason for going: 買(か)い物(もの)に行(い)く, to go shopping. Here the purpose is 包丁研(ほうちょうと)ぎ.
行(い)ってる is the casual contraction of 行(い)っている. With 行(い)く, ている describes the state after leaving, so it means “has gone and is there now”, not “is on the way”. Hakumei is out of the house.
The わ at the end softens Mikochi’s statement. It’s part of her ordinary speaking style.

4そういえば〜は？ = by the way, what about ~?

そういえば brings up something the conversation just reminded the speaker of. Konju’s question stops at は, leaving out どこにいるの or a similar ending. A rising tone on 〜は？ is enough to ask where someone is or how something stands.

そういえば (Come to think of it): そういえば brings up something the speaker has just been reminded of, like “come to think of it” or “speaking of which”. It often opens a change of subject.
包丁 (Kitchen knife): 包丁(ほうちょう) is the knife used for cooking. Kinds are named by what they cut, such as a 出刃包丁(でばぼうちょう) for fish.
研ぐ (To sharpen): 研(と)ぐ is to sharpen a blade by rubbing it on a whetstone, as in 包丁(ほうちょう)を研(と)ぐ. With rice, it means to wash the grains by rubbing them together in water: 米(こめ)を研(と)ぐ.
行く (To go): 行(い)く means to go or move toward a place away from the speaker.